P is a polynomial of degree 6. M and N are two real numbers with 0 < M < N. Given that:

1. P(M) = P(-M), and:
2. P(N) = P(-N)
3. P’(0) = 0

Does the relationship P(x) = P(-x) hold for all nonzero real values of x?
If so, prove it.
If not, provide a counterexample.

(In reply to Counter Counter example (spoiler) by Steve Herman)

Although my answer was sent in a haste thru my smartphone,

without any explanation, I still do not see where I have erred:

Assuming  C<>M &   C<>N     <> meaning non-equal

Then  P(M)=P(-M)=P(N)=P(-N)=P(C)=0

While P(-C)=-C*(C^2-M^2)*(C^2-N^2)*(-2C) <>0

SO:    P(C)=0  WHILE P(-C)<>0

PLEASE COMMENT.

Posted by Ady TZIDON on 2015-05-13 11:41:01