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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?  ]
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$p_{2}(x)=x, p_{3}(x)=x^{2}-1 / 3$
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