Work out the values of a, b and c

I feel stupid: six years of high-school math and I still can't solve this problem.

Hopefully, there is someone on this forum who can!

Problem:

Let V(p) = ap^{2}+ bp + c

V(0) = 0 and V(1) = 0.

Work out (without a calculator) the values of a, b and c.

Re: Work out the values of a, b and c

$\displaystyle V(0) = a(0)^2+b(0)+c = c = 0$

now you do the same for V(1) and then solve for * a* and *b*

Re: Work out the values of a, b and c

However, in general, and in this problem in particular, two equations are not enough to determine **three** values. There are an infinite number of values of a and b that, with c= 0, satisfy these conditions.