Consider the function, prove that it's bilinear, symmetric, and positive definite

[Orthogonal Polynomials]. Consider the following bi-valued function defined on the space of polynomials of degree ≤ 2:
 (Image 1)

For whichever polynomials p(x), q(x) ∈ P≤2. Consider the following polynomials:

p0(x) = 1,   p1(x) = x,   p2(x) = (3/2 )x² − 1/2 .

(a) Prove that F is bilinear, symmetric, and positive definite
(b) Prove that the family (p0, p1, p2) is an orthogonal basis of P≤2.


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