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The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\). \(S_1\): there exists \(x_1, x_2 \in(2,4), x_1 \(S_2…

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The function \(f(x)=x^3-6 x^2+a x+b\) is such that \(f(2)=f(4)=0\).
\(S_1\): there exists \(x_1, x_2 \in(2,4), x_1\(S_2\): there exists \(x_3, x_4 \in(2,4), x_3

[JEE Main 2021, 1 Sep (Shift 2)]

a

both \(S_1\) and \(S_2\) are true

b

\(S_1\) is true and \(S_2\) is false

c

\(S_1\) is false and \(S_2\) is true

d

both \(S_1\) and \(S_2\) are false

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