# Weird Roots

Calculus Level 5

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:

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