Let , , , and . If only for and , then the value of…

MATHEMATICS · Single correct · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Let

a\ne a_1

f(x)=ax^2+bx+c

g(x)=a_1x^2+b_1x+c_1

, and

p(x)=f(x)-g(x)

. If

p(x)=0

only for

x=-1

and

p(-2)=2

, then the value of

p(2)

is (1) 18 (2) 3 (3) 9 (4) 6