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 286: 122



Work Step by Step

If $i$ is a zero of $f$ then the complex conjugate $-i$ is also a zero. We have three zeros ($2,~i,~-i$). We can find a three-degree polynomial. $f(x)=a(x-2)[(x-i)[x-(-i)]$ $f(x)=a(x-2)(x^2-i^2)$ $f(x)=a(x-2)(x^2+1)$ $f(x)=a(x^3+x-2x^2-2)$ $f(x)=a(x^3-2x^2+x-2)$ $a=-1$ $f(x)=-1(x^3-2x^2+x-2)$ $f(x)=-x^3+2x^2-x+2$
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