SOLUTION: P(x) is a polynomial such that: P(x + 3/2)=P(x) If P(17) = 687, find the value of P(23).

Algebra ->  Proofs -> SOLUTION: P(x) is a polynomial such that: P(x + 3/2)=P(x) If P(17) = 687, find the value of P(23).      Log On


   

Question 974259: P(x) is a polynomial such that: P(x + 3/2)=P(x)
If P(17) = 687, find the value of P(23).
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I don't think a polynomial like that exists, because
a P%28x%29 such that P%28x+%2B+3%2F2%29=P%28x%29 is a periodic function (like trigonometric functions),
that has a period of 3%2F2 or 3%2F%222+n%22 for a natural number n .

For such a function,
P%2823%29=P%2817%29=687 ,
because 23-17=6=4%2A%283%2F2%29 , so P%2823%29=P17%2B4%283%2F2%29%29 and