( a) Explanation The quadratic equation a x 2 + b x + c = 0 can be solved by the quadratic formula given as: x = − b ± b 2 − 4 a c 2 a Where a , b and c are any real numbers. The quantity b 2 − 4 a c under the radical sign is known as the discriminant of the equation. The discriminant can be used to determine the number of real, repeated and imaginary solutions, that is: i If the discriminant b 2 − 4 a c is greater than 0 , then the quadratic equation a x 2 + b x + c = 0 will have 2 real solutions. ii If the discriminant b 2 − 4 a c is equal to 0 , then the quadratic equation a x 2 + b x + c = 0 will have 1 real repeated solution. iii If the discriminant b 2 − 4 a c is less than 0 , then the quadratic equation a x 2 + b x + c = 0 will have 2 imaginary solutions ( b) To determine The number of real and imaginary solutions of the quadratic equation 9 x 2 + 6 x + 1 = 0 by the use of the discriminant method. ( c) To determine The number of real and imaginary solutions of the quadratic equation 9 x 2 + 2 x + 1 = 0 by the use of the discriminant method.

10th Edition

ISBN: 8220103611893

Author: Larson

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Roots

Videos

Question

Chapter 4.2, Problem 2ECP

( a)

To determine

The number of real and imaginary solutions of the quadratic equation 3x2+2x−1=0 by the use of the discriminant method.

( b)

To determine

The number of real and imaginary solutions of the quadratic equation 9x2+6x+1=0 by the use of the discriminant method.

( c)

To determine

The number of real and imaginary solutions of the quadratic equation 9x2+2x+1=0 by the use of the discriminant method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.2, Problem 1ECP

Chapter 4.2, Problem 3ECP

Students have asked these similar questions

Please help me answer this question!. Please handwrite it. I don't require AI answers. Thanks for your time!.

1 What is the area of triangle ABC? 12 60° 60° A D B A 6√√3 square units B 18√3 square units 36√3 square units D 72√3 square units

Par quel quadrilatère est-elle représentée sur ce besoin en perspective cavalière

Chapter 4 Solutions

EBK TRIGONOMETRY

Ch. 4.1 - Perform each operation and write the result in...Ch. 4.1 - Prob. 2ECP Ch. 4.1 - Prob. 3ECP Ch. 4.1 - Prob. 4ECP Ch. 4.1 - Prob. 5ECP Ch. 4.1 - Prob. 6ECP Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E

Knowledge Booster

$Geometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

The number of real and imaginary solutions of the quadratic equation 3 x 2 + 2 x − 1 = 0 by the use of the discriminant method.

Solution Summary: The author explains how the quadratic equation ax2+bx+c=0 can be solved using the discriminant method.

Concept explainers

Videos

The number of real and imaginary solutions of the quadratic equation 3x2+2x−1=0 by the use of the discriminant method.

The number of real and imaginary solutions of the quadratic equation 9x2+6x+1=0 by the use of the discriminant method.

The number of real and imaginary solutions of the quadratic equation 9x2+2x+1=0 by the use of the discriminant method.

Want to see the full answer?

Chapter 4 Solutions