Answer
$ p(x)=x^2+2x-3$.
Work Step by Step
We have
$$ p(x)=x^2+ax+b, \quad p'(x)= 2x+a.$$
Since, $ p(1)=0$ and $ p'(1)=4$, we get the equations
$$ a+b=-1, \quad a=2$$
Hence we have the solution $ a=2, b=-3$. Then, $ p(x)=x^2+2x-3$.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Exercises - Page 115: 53
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