solving the following equation $\sum_{k=1}^nt_k^2(\alpha_k-x)^2=\prod_{k=1}^n(\alpha_k-x)^2$

Question

let $\alpha_1,\alpha_2,...,\alpha_n$ be non-negative numbers and $t_1^2+t_2^2+...+t_n^2=1$ is it possible to solve this equation

$$\sum_{k=1}^nt_k^2(\alpha_k-x)^2=\prod_{k=1}^n(\alpha_k-x)^2$$