The quadratic polynomial P(x) has a zero at

Erika Bernard

Erika Bernard

Answered question

2022-04-10

The quadratic polynomial P(x) has a zero at x=2. The polynomial P(P(x)) has only one real zero at x=5. Compute P(0).

Answer & Explanation

superpms01wks1

superpms01wks1

Beginner2022-04-11Added 13 answers

P(x) will be of the form
P(x)=(x2)(ax+b).
Let c=P(5)=3(5a+b).
then the equation P(P(5))=(c2)(ac+b)
=ac2+(b2a)c2b=0
has only one root if the discriminant is zero.
Δ=(b+2a)2=0b=2a
and c=2ab2a=2
but c=3(5a+b)=9a=2
finally a=29;;,;;b=49;;
P(x)=29(x-2)2
P(0)=89.

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