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| Multiply The Derivatives, Get Polynomial (Posted on 2007-09-25) |
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Find all polynomials H(x) such that:
H(2x) = H'(x)*H"(x)
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Submitted by K Sengupta
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Rating: 3.2000 (5 votes)
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Solution:
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(Hide)
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Except for the trivial case H(x)=0, the only nontrivial polynomial that satisfies the equation is
H(x) = 4x3/9
EXPLANATION:
Refer to the solution posted by Mike C in this location.
Chesca Ciprian solves the general case of determining all possible polynomials H(x) satisfying:
H(nx) = H'(x)*H''(x), where n is a positive integer - in this location.
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