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: 42



Work Step by Step

If $-3i$ is a zero of $f$ then the complex conjugate $3i$ is also a zero. $f(x)=a(x-4)(x-3i)[x-(-3i)]$ $f(x)=a(x-4)(x-3i)(x+3i)$ $f(x)=a(x-4)[x^2-(3i)^2]$ $f(x)=a(x-4)(x^2+9)$ $f(x)=a(x^3+9x-4x^2-36)$ We can choose any value for $a$. So, let's make $a=1$ $f(x)=x^3-4x^2+9x-36$
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