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(a) Define an inner product on P3 by (f,g) = f* f(x)g(x) dx. = Find a polynomial f(x) ax² + bx + e, where a, b, e € R, which is orthogonal to both polynomials g(x) = c + 1 and h(x) = (c+1)x. Also, calculate the length of h(x).

(a) Define an inner product on P3 by (f,g) = f* f(x)g(x) dx. = Find a polynomial f(x) ax² + bx + e, where a, b, e € R, which is orthogonal to both polynomials g(x) = c + 1 and h(x) = (c+1)x. Also, calculate the length of h(x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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C=4 please give me a answer of part a within 15 minutes
(a) Define an inner product on P3 by (f.g) = f* f(x)g(x) dx. Find a polynomial f(x) = ax² + bx + e, where a, b, e € R, which is orthogonal to both polynomials g(x) = c+1 and h(x) = (c+1)x. Also, calculate the length of h(x). (b) Use the rotation matrix and find the new (transformed) coordinates of P(c + 1, √3) when it is rotated counterclockwise by.
Transcribed Image Text:(a) Define an inner product on P3 by (f.g) = f* f(x)g(x) dx. Find a polynomial f(x) = ax² + bx + e, where a, b, e € R, which is orthogonal to both polynomials g(x) = c+1 and h(x) = (c+1)x. Also, calculate the length of h(x). (b) Use the rotation matrix and find the new (transformed) coordinates of P(c + 1, √3) when it is rotated counterclockwise by.
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