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Using the inner product \(\langle f, g\rangle=\int_{-1}^{1} f(x) g(x) d x\), for which values of the real constants \(\alpha, \beta, \gamma\) are the quadratic polynomials ...

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Using the inner product \(\langle f, g\rangle=\int_{-1}^{1} f(x) g(x) d x\), for which values of the real constants \(\alpha, \beta, \gamma\) are the quadratic polynomials \(p_{1}(x)=1, \quad p_{2}(x)=\alpha+x \quad p_{3}(x)=\beta+\gamma x+x^{2}\) orthogonal?  ]
in Mathematics by Platinum (102k points) | 243 views

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ANSWER:

\( p_{2}(x)=x, p_{3}(x)=x^{2}-1 / 3 \)
by Platinum (102k points)

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