JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 26

Let $f$ and $g$ be twice differentiable even functions on $(-2,2)$ such that $f\left(\frac14\right)=0$, $f\left(\frac12\right)=0$, $f(1)=1$ and $g\left(\frac34\right)=0$, $g(1)=2$. Then, the minimum number of solutions of $f(x)g''(x)+f'(x)g'(x)=0$ in $(-2,2)$ is equal to ______.