# Let equation $\sum_{k=0}^n\begin{pmatrix} n\\k\end{pmatrix} ^2x^{n-k}=0$. Proved that…

Problem:

Proved that with all n is positive integer, let equation:

$$\begin{pmatrix} n\\0\end{pmatrix} ^2x^n+\begin{pmatrix} n\\1\end{pmatrix} ^2x^{n-1}+\cdots+\begin{pmatrix} n\\n\end{pmatrix} ^2=0$$

Have n real-root diacritical and which are all negative real root!

P.s

• @BettyMock You got it wrong, a negative root $-a$ yields a factor $x+a$, in the product everything will be positive and allright. – Ewan Delanoy Nov 30 '13 at 6:35