SOLUTION: Suppose P(x) is a quadratic polynomial (highest degree of 2) satisfying P(P(x)) - (P(x))^2 = x^2 + x + 2016 for all real x. Find P(x). Express the answer as a quadratic polynomial

Question 1207386: Suppose P(x) is a quadratic polynomial (highest degree of 2) satisfying
P(P(x)) - (P(x))^2 = x^2 + x + 2016 for all real x. Find P(x). Express the answer as a quadratic polynomial with highest degree of 2.
I've been stuck on this one for a while now and haven't found anything useful to solve. Can anyone help me out? Thanks in advance!
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let

Then

We need to have

On the left hand side of the equation, is going to give and terms; but there are no terms of that degree on the right hand side. That means we must have (a-1)=0, or a=1.

Then

Equating the coefficients of x^2 on the two sides of the equation, we need to have

and since a=1, b=1 also. And now, with a=1 and b=1, we have

And we have the polynomial we need.

ANSWER:

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