Taking

q (x) = 1

q (x) = x

and

q (x) = x^{2}

in equation (1) and working out the integral (easy!) will give you three equations which you can solve to find

λ_{1}, λ_{2}

and

λ_{3}

The key to showing that the same formula works for other polynomials is to show that if it works for $1, x$ and $x^{2}$ it works for any linear combination of them and so for any quadratic polynomial.

Finally you can go on to check out the formula for $x^{3}, x^{4}$ and $x^{5}$ .