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

Given that:

- P(M) = P(-M), and:
- P(N) = P(-N)
- 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.**