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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!