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Find the value of P(0)

Source: MTRP 2016 Class 11-Multiple Choice Question: Problem 13 :-

May 31, 2020
quadraticsalgebra

Problem Statement

Let P(x)=x2+bx+cP(x)=x^2+bx+c. Suppose P(P(1))=P(P(−2))=0P(P(1))=P(P(-2))=0 and P(1)≠P(−2)P(1)\neq P(-2). Then P(0)=P(0)=
[*] −52-\frac{5}{2}
[*] −32-\frac{3}{2}
[*] −74-\frac{7}{4}
[*] 67\frac{6}{7}
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