WBJEE · Maths · Application of Derivatives
Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in R .\) 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)
Answer & Solution
Correct Answer
(B) \(f(x)\) has exactly one zero in (1,2) if \(-1 < c < 0\)
Step-by-step Solution
Detailed explanation
Given, \[ \begin{array}{ll} f(x) & =x^{4}-4 x^{3}+4 x^{2}+c \\ f(1) & =1+c \\ \text { and } \quad f(2) & =2^{4}-4(2)^{3}+4(2)^{2}+c \end{array} \]…
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