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Chebyshev polynomial question

I am trying to prove a property of Chebyshev polynomials.

Given the polynomials $T_n(x), n = 0, 1, \ldots$ which are recursively defined by $$\begin{cases} T_0(x) = 1\\ T_1(x) = x \\T_n(x) = 2x T_{n−1}(x) − T_{n−2}(x), & \text{for } n \geq 2\end{cases}$$

Show that $T_n(x)= 2^{n−1}(x−x_0)(x−x_1)\cdots(x−x_{n−1})$,, where $x_0,\ldots,x_{n-1}$ are the roots of the polynomial.

I am not even sure how to get started on this and would appreciate any help!

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    What are $x_0,x_1,...$? Do you want to prove that the roots of $T_n(x)$ are real numbers? In fact, the roots are simply roots and they are in $(-1,1)$.2012-09-10

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