Question

Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in \mathbb{R}\). Then
(A) \(f(x)\) has infinitely many zeros in \((1,2)\) for all \(c\)
(B) \(f(x)\) has exactly one zero in \((1,2)\) if \(-1<c<0\)
(C) \(f(x)\) has double zeros in \((1,2)\) if \(-1<c<0\)
(D) Whatever be the value of \(c, f(x)\) has no zero in \((1,2)\)
Ans: (B)

Answer 1

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