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: 41



Work Step by Step

If $5i$ is a zero of $f$ then the complex conjugate $-5i$ is also a zero. $f(x)=a(x-1)(x-5i)[x-(-5i)]$ $f(x)=a(x-1)(x-5i)(x+5i)$ $f(x)=a(x-1)[x^2-(5i)^2]$ $f(x)=a(x-1)(x^2+25)$ $f(x)=a(x^3+25x-x^2-25)$ We can choose any value for $a$. So, let's make $a=1$ $f(x)=x^3-x^2+25x-25$
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