(Algebra: solve quadratic equations) The two roots of a quadratic equation ax + bx + c = 0 can be obtained using the following formula: -b + Vb – 4ac and -b – Vb? rɔ = 4ас | 2a 2a 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"

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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3.1 Please take screenshots show the steps and results.

**Debugging Tip:**  
Before you ask for help, read and explain the program to yourself, and trace it using several representative inputs by hand or using an IDE debugger. You learn how to program by debugging your own mistakes.

### Algebra: Solve Quadratic Equations

The two roots of a quadratic equation \( ax^2 + bx + c = 0 \) can be obtained using the following formula:

\[
r_1 = \frac{{-b + \sqrt{{b^2 - 4ac}}}}{2a} \quad \text{and} \quad r_2 = \frac{{-b - \sqrt{{b^2 - 4ac}}}}{2a}
\]

\( b^2 - 4ac \) 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 that you can use `Math.pow(x, 0.5)` to compute \( \sqrt{x} \). Here are some sample runs.
Transcribed Image Text:**Debugging Tip:** Before you ask for help, read and explain the program to yourself, and trace it using several representative inputs by hand or using an IDE debugger. You learn how to program by debugging your own mistakes. ### Algebra: Solve Quadratic Equations The two roots of a quadratic equation \( ax^2 + bx + c = 0 \) can be obtained using the following formula: \[ r_1 = \frac{{-b + \sqrt{{b^2 - 4ac}}}}{2a} \quad \text{and} \quad r_2 = \frac{{-b - \sqrt{{b^2 - 4ac}}}}{2a} \] \( b^2 - 4ac \) 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 that you can use `Math.pow(x, 0.5)` to compute \( \sqrt{x} \). Here are some sample runs.
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