If \( f(x)=(x-a)(x-b) \) for \( a, b \in R \), then minimum number of roots of equation
\( \pi\l... VIDEO
If \( f(x)=(x-a)(x-b) \) for \( a, b \in R \), then minimum number of roots of equation
\( \pi\left(f^{\prime}(x)\right)^{2} \cos (\pi f(x))+\sin (\pi f(x)) \cdot f^{\prime \prime}(x)=0 \) in \( (\alpha, \beta) \),
where \( f(\alpha)=3=f(\beta) \) is ......... (here, \( \alphaab\beta \) )
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