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: 48



Work Step by Step

If $\sqrt 2i$ is a zero of $f$ then the complex conjugate $-\sqrt 2i$ is also a zero. $f(x)=a[(x-(-1)](x-2)(x-\sqrt 2i)[x-(-\sqrt 2i)]$ $f(x)=a(x+1)(x-2)(x-\sqrt 2i)(x+\sqrt 2i)$ $f(x)=a(x^2-2x+x-2)[x^2-(\sqrt 2i)^2]$ $f(x)=a(x^2-x-2)(x^2+2)$ $f(x)=a(x^4+2x^2-x^3-2x-2x^2-4)=a(x^4-x^3-2x-4)$ $f(1)=a(1^4-1^3-2(1)-4)=12$ $a(-6)=12$ $a=-2$ $f(x)=-2(x^4-x^3-2x-4)$ $f(x)=-2x^4+2x^3+4x+8$
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