Orthogonal polynomials (was Chebyshv, etc.)

Checkiong Wikipedia, I realized there are many more mysteries on those. For instance , all those polynomials (of degree n) (like Legendre, Chebyshev, Hermite, etc.) have n real roots in the interval of integration. Any simple proof?
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Relevant Pages

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  • Re: Orthogonal polynomials (was Chebyshv, etc.)
    ... For instance, all those polynomials (like Legendre, Chebyshev, Hermite, etc.) have n real roots in the interval of integration. ...
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