Given $\pi a^2-\pi a b=30 \pi$ and $\pi a b-\pi b^2=18 \pi$ on subtracting, we get $(a-b)^2=a^2-2 a b+b^2=12$ Let $f$ and $g$ be twice differentiable even functions on $(-2,2)$ such that $f\left(\frac{1}{4}\right)=0, f\left(\frac{1}{2}\right)=0, f(1)=1$ and $g\left(\frac{3}{4}\right)=0, g(1)=2$. Then, the minimum number of solutions of $f(x) g^{\prime \prime}(x)+f^{\prime}(x) g^{\prime}(x)=0$ in (-2,2) is equal to $\_\_\_\_$ .