p(x) is a polynomial satisfying $p (x + \frac{3}{2}) = p (x)$ , for all real values of 'x'. If p(5)=2010, what is the value of p(8)?

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Solution

The correct option is A
Given relation : $p + (x + (\frac{3}{2})) = p (x)$ .
Also: p(5) = 2010.
So, $p (5) = p + (5 + (\frac{3}{2})) = p (6.5) = 2010$ .
And, $p (6.5) = p (6.5 + (\frac{3}{2}) = p (8) = 2010$ .
So, p(8) = 2010.

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