P is a polynomial of degree 6. M and N are two real numbers with 0 < M < N.
- 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
While P(-C)=-C*(C^2-M^2)*(C^2-N^2)*(-2C) <>0
SO: P(C)=0 WHILE P(-C)<>0