( Algebra: solve quadratic equations ) The two roots of a quadratic equation ax 2 + bx + c = 0 can be obtained using the following formula: r 1 = − b + b 2 − 4 a c 2 a and r 2 = − b − b 2 − 4 a c 2 a b 2 − 4 ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots. Write a program that prompts the user to enter values for a , b and c and displays the result based on the discriminant. If the discriminant is positive, display two roots. If the discriminant is 0, display one root. Otherwise, display “The equation has no real roots.” Note you can use Math. pow(x, 0.5) to compute x . Here are some sample runs:

Question

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Answer 1

Textbook Question

Chapter 3, Problem 3.1PE

(Algebra: solve quadratic equations) The two roots of a quadratic equation ax² + bx + c = 0 can be obtained using the following formula:

r 1 = − b + b 2 − 4 a c 2 a and r 2 = − b − b 2 − 4 a c 2 a

b² − 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots.

Write a program that prompts the user to enter values for a, b and c and displays the result based on the discriminant. If the discriminant is positive, display two roots. If the discriminant is 0, display one root. Otherwise, display “The equation has no real roots.”

Note you can use Math. pow(x, 0.5) to compute x . Here are some sample runs:

Chapter 3, Problem 3.1PE, (Algebra: solve quadratic equations) The two roots of a quadratic equation ax2 + bx + c = 0 can be

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

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05:55

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Answer 2

Textbook Question

Chapter 3, Problem 3.1PE

(Algebra: solve quadratic equations) The two roots of a quadratic equation ax² + bx + c = 0 can be obtained using the following formula:

r 1 = − b + b 2 − 4 a c 2 a and r 2 = − b − b 2 − 4 a c 2 a

b² − 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots.

Write a program that prompts the user to enter values for a, b and c and displays the result based on the discriminant. If the discriminant is positive, display two roots. If the discriminant is 0, display one root. Otherwise, display “The equation has no real roots.”

Note you can use Math. pow(x, 0.5) to compute x . Here are some sample runs:

Chapter 3, Problem 3.1PE, (Algebra: solve quadratic equations) The two roots of a quadratic equation ax2 + bx + c = 0 can be

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

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05:55

Answer 3

Textbook Question

Chapter 3, Problem 3.1PE

(Algebra: solve quadratic equations) The two roots of a quadratic equation ax² + bx + c = 0 can be obtained using the following formula:

r 1 = − b + b 2 − 4 a c 2 a and r 2 = − b − b 2 − 4 a c 2 a

b² − 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots.

Write a program that prompts the user to enter values for a, b and c and displays the result based on the discriminant. If the discriminant is positive, display two roots. If the discriminant is 0, display one root. Otherwise, display “The equation has no real roots.”

Note you can use Math. pow(x, 0.5) to compute x . Here are some sample runs:

Chapter 3, Problem 3.1PE, (Algebra: solve quadratic equations) The two roots of a quadratic equation ax2 + bx + c = 0 can be

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

05:55

Answer 4

Textbook Question

Chapter 3, Problem 3.1PE

(Algebra: solve quadratic equations) The two roots of a quadratic equation ax² + bx + c = 0 can be obtained using the following formula:

r 1 = − b + b 2 − 4 a c 2 a and r 2 = − b − b 2 − 4 a c 2 a

b² − 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no real roots.

Write a program that prompts the user to enter values for a, b and c and displays the result based on the discriminant. If the discriminant is positive, display two roots. If the discriminant is 0, display one root. Otherwise, display “The equation has no real roots.”

Note you can use Math. pow(x, 0.5) to compute x . Here are some sample runs:

Chapter 3, Problem 3.1PE, (Algebra: solve quadratic equations) The two roots of a quadratic equation ax2 + bx + c = 0 can be

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

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05:55

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

Answer 8

Expert Solution & Answer

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Program Description Answer

The below program is used to solve the quadratic equation:

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Program Plan Intro

Algebra: solve quadratic equation

Program Plan:

Import the required packages.
Create a class Exercise
- Define the main method.
- Define the scanner input and prompt user to enter the value of a,b,c.
- Get the input.
- Calculate the discriminant value.
- Condition to validate the discriminant value.
- After validation the value gets of the root gets calculated based on the condition.
- Display the result of roots.

Answer 12

Program Description Answer

The below program is used to solve the quadratic equation:

Answer 13

Explanation of Solution

Program:

//import the required packages

import java.util.Scanner;

//define the class exercise

public class Exercise

{

public static void main(String[] args)

{

//scanner input

Scanner input = new Scanner(System.in);

/*prompt user to enter the value of the a,b and c*/

System.out.print("Enter a, b, c: ");

//get value of a

double a = input.nextDouble();

//get value of b

double b = input.nextDouble();

//get value of c

double c = input.nextDouble();

//equation to calculate the discriminant

double discriminant = b * b - 4 * a * c;

//condition to validate the discriminant value

if (discriminant < 0)

{

//display result

System.out.println("The equation has no real roots");

}

//condition to validate the discriminant value

else if (discriminant == 0)

{

//equation to calculate the root value

double r1 = -b / (2 * a);

//display result

System.out.println("The equation has one root " + r1);

}

//condition to validate the discriminant value

else

{

// (discriminant > 0)

//equation to calculate the root value

double r1 = (-b + Math.pow(discriminant, 0.5)) / (2 * a);

//equation to calculate the root value

double r2 = (-b - Math.pow(discriminant, 0.5)) / (2 * a);

//display result

System.out.println("The equation has two roots " + r1 + " and " + r2);

}

Answer 14

Sample Output

Enter a, b, c: 1

2.0

1

The equation has one root -1.0

Additional Output 1:

Enter a, b, c: 1.0

3

1

The equation has two roots -0.3819660112501051 and -2.618033988749895

Additional Output 2:

Enter a, b, c: 1

2

3

The equation has no real roots

Answer 15

Ch. 3.2 - List six relational operators.Ch. 3.2 - Assuming x is 1, show the result of the following...Ch. 3.2 - Can the following conversions involving casting be...Ch. 3.3 - Write an if statement that assigns 1 to x if y is...Ch. 3.3 - Write an if statement that increases pay by 3% if...Ch. 3.3 - Prob. 3.3.3CP Ch. 3.4 - Write an if statement that increases pay by 3% if...Ch. 3.4 - What is the output of the code in (a) and (b) if...Ch. 3.5 - Prob. 3.5.1CP Ch. 3.5 - Suppose x = 2andy = 3. Show the output, if any, of...

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