Let f and g be twice differentiable even functions on (-2,2) such that f(1/4)=0, f(1/2)=0, f(1)=1 and g(3/4)=0, g(1)=2 Then, the minimum number of…

Let $\displaystyle f$ and $\displaystyle g$ be twice differentiable even functions on $\displaystyle (-2,2)$ such that $$f\left(\frac{1}{4}\right)=0, f\left(\frac{1}{2}\right)=0, f(1)=1 \text { and } g\left(\frac{3}{4}\right)=0, g(1)=2 $$ Then, the minimum number of solutions of $\displaystyle f(x) g^{\prime \prime}(x)+f^{\prime}(x) g^{\prime}(x)=0$ in ( $\displaystyle -2,2$ ) is equal to \_\_\_\_.