Answer
$f(x)=x^2-8x+13$
Work Step by Step
$f(x)=a[x-(4+\sqrt 3)][x-(4-\sqrt 3)]=a[(x-4)-\sqrt 3][(x-4)+\sqrt 3]=a[(x-4)^2-(\sqrt 3)^2]=a(x^2-8x+16-3)=a(x^2-8x+13)$
$a$ can be any value. If $a=1$:
$f(x)=x^2-8x+13$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 3 - 3.2 - Polynomial Functions of Higher Degree - 3.2 Exercises - Page 261: 60
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