Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.4 - Zeroes of Polynomial Functions - 3.4 Exercises - Page 284: 47



Work Step by Step

If $i$ is a zero of $f$ then the complex conjugate $-i$ is also a zero. $f(x)=a[(x-(-2)](x-1)(x-i)[x-(-i)]$ $f(x)=a(x+2)(x-1)(x-i)(x+i)$ $f(x)=a(x^2-x+2x-2)[x^2-i^2]$ $f(x)=a(x^2+x-2)(x^2+1)$ $f(x)=a(x^4+x^2+x^3+x-2x^2-2)=a(x^4+x^3-x^2+x-2)$ $f(0)=a(0^4+0^3-0^2+0-2)=-4$ $a(-2)=4$ $a=-2$ $f(x)=-2(x^4+x^3-x^2+x-2)$ $f(x)=-2x^4-2x^3+2x^2-2x+4$
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