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Sextic Settlement (Posted on 2015-05-13) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Counterexample | Comment 4 of 6 |
(In reply to re: Counterexample by Steve Herman)

I think you mean the third condition rather than the first.
  Posted by Charlie on 2015-05-13 11:20:47

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