If $\frac\pi2\lt\theta\lt\pi$, find the number of solutions of $x^2+x+\frac{\cos\theta}2=0$

Question

If $\frac\pi2\lt\theta\lt\pi$, find the number of solutions of $x^2+x+\frac{\cos\theta}2=0$

$\cos\theta$ varies between $-1$ to $0$. Thus, $x^2+x$ should vary between $0$ to $\frac12$.

Thus, I think the number of solutions are infinite. But the answer given is $2$.

Answer 1

Hint: the solution sought are in $x$ and this is a quadratic equation. Thus the number of solutions depends on the usual sign of the discriminant $\Delta$... can you take it from here?