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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
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

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