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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