AP EAMCET · Maths · Differentiation
If \(x=a\) is a root of multiplicity two of a polynomial equation \(f(x)=0\), then
- A \(f^{\prime}(a)=f^{\prime \prime}(a)=0\)
- B \(f^{\prime \prime}(a)=f(a)=0\)
- C \(f^{\prime}(a) \neq 0 \neq f^{\prime \prime}(a)\)
- D \(f(a)=f^{\prime}(\mathrm{a})=0 ; f^{\prime \prime}(a) \neq 0\)
Answer & Solution
Correct Answer
(D) \(f(a)=f^{\prime}(\mathrm{a})=0 ; f^{\prime \prime}(a) \neq 0\)
Step-by-step Solution
Detailed explanation
Given that, \(x=a\) is a root of multiplicity two of a polynomial equation \(f(x)=0\). Let \(f(x)=(x-a) g(x)\) On differentiating w.r.t. \(x\), we get \(\Rightarrow f^{\prime}(x)=2(x-a) g(x)+(x-a)^2 g^{\prime}(x)\) Again, differentiating w.r.t \(x\), we get…
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