If $f(x)= (x-a)(x-b)$ for $a,b$ $\in \mathbb{R}$ then the minimum number of roots of equation
$$\pi(f'(x))^2 \cos(\pi(f(x))) + \sin(\pi(f(x)))f''(x) =0$$
in $(\alpha,\beta)$ where $f(\alpha) =+3 = f(\beta)$ and $\alpha <a<b<\beta$ will be:
BTW the notation confused me quite a bit. The notation $\pi(f'(x))$ looks as if $\pi$ is a function. The OP probably means just $\pi$ multiplied by $f'(x)$.
Let's see whether other people who visit this room have also some suggestion for suitable tags. (That's my best guess what Arjun wanted to ask about.)
If $f(x)= (x-a)(x-b)$ for $a,b$ $\in \mathbb{R}$ then the minimum number of roots of equation
$$\pi(f'(x))^2 \cos(\pi(f(x))) + \sin(\pi(f(x)))f''(x) =0$$
in $(\alpha,\beta)$ where $f(\alpha) =+3 = f(\beta)$ and $\alpha <a<b<\beta$ will be:
If $f(x)= (x-a)(x-b)$ for $a,b$ $\in \mathbb{R}$ then the minimum number of roots of equation
$$\pi(f'(x))^2 \cos(\pi(f(x))) + \sin(\pi(f(x)))f''(x) =0$$
in $(\alpha,\beta)$ where $f(\alpha) =+3 = f(\beta)$ and $\alpha <a<b<\beta$ will be:
