Let , where , and are real…

MATHEMATICS · Multi-part · AoPS · Mathematics · More Variables · More Variables

Problem

Let

p(x)=ax^{4}+bx^{2}+c

, where

a

b

and

c

are real constants. (i) Write

p(2)

in terms of

a

b

and

c

. (ii) If

a=1

b=-3

and

c=5

, compute the numerical value of

p(2)

. (iii) Suppose

p(2)=0

. Using your expression from part (i), obtain a relation among

a

b

and

c

that must hold for this condition to be satisfied.