perplexus.info :: Just Math : Shared roots from a quadratic

Shared roots from a quadratic (Posted on 2024-06-21)

P(x) is a monic trinomial of degree 2 such that P(x) and P(P(P(x))) share a root. Prove that P(0)*P(1)=0.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

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a start

| Comment 1 of 2

P(x) = x^2 + bx + c

P(0)*P(1) = c(1+b+c) which is 0 if c = {0, -(b+1)}

But since it is a trinomial then c cannot be zero.

So if it can be shown that P(x) and P(P(P(x))) share a root

iff (1+b+c) = 0, then that will constitute a proof.

Posted by Larry on 2024-06-21 13:03:08

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