Quasi-concavity of a function

Question

I'm trying to show the following function is quasi-concave in $x$ $$\sum^n_{i=0}{n\choose i}F(x)^{i}(1-F(x))^{n-i}u(i)$$ Here, $x$ is defined on $[0,1]$ and $F$ maps $[0,1]$ to $[0,1]$, and is a strictly increasing in $x$. So, the function is a convex combination of $u(1)$ to $u(n)$, and I want to know whether the function is quasi-concave in the weights.