Fp(x) and q(x) are arbitrary polynomials of degreeat most 2, then the mapping< p, q > = p(-2)q(-2)+ p(0)q(0)+ p(2)q(2)defines an inner product in p3.use this inner product to find < p, q > , llpll, llqll, and the angletetha, between p(x) and q(x) forp(x) = 2x^2+6x+1 and q(x) = 3x^2-5x-6.< p; q > = ? llpll = ? llqll= ?

We're given an inner product defined by

That is, we multiply the values of and at and add those products together.

The inner product is

To find the norms and , recall that the dot product of a vector with itself is equal to the square of that vector's norm:

So we have

Finally, the angle between and can be found using the relation

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step-by-step explanation:

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