   Chapter 8.4, Problem 27E

Chapter
Section
Textbook Problem

Derive the quadratic formula for the zeros of a x 2 + b x + c , where a ,   b and c are complex numbers and a ​   ≠   0 .

To determine

The quadratic formula for the zeros of ax2+bx+c, where a,b, and c are complex numbers and a0.

Explanation

Let f(x)=ax2+bx+c

To find zeros of f(x),

Consider, f(x)=ax2+bx+c=0

Subtract c from both sides,

(ax2+bx+c)c=c

ax2+bx=c

As a0, divide both sides by a,

ax2a+bxa=ca

x2+(ba)x=ca

By adding b24a2 on both sides,

x2+(ba)x+b24a2=ca+b24a2

x2+(ba)x+b24a2=4ac4a2+b24

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Problems 7-34, perform the indicated operations and simplify. 17.

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate Evaluate the expression. 14. 642/3

Precalculus: Mathematics for Calculus (Standalone Book)

If limx1f(x)8x1=10, find limx1f(x).

Single Variable Calculus: Early Transcendentals, Volume I

For y=12gt2 (where g is a constant), dydt=. a) 14g2 b) 12g c) gt d) gt2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: is a geometric series.

Study Guide for Stewart's Multivariable Calculus, 8th 