JEE Mains · Maths · STD 12 - 6. Application of derivatives
Suppose \(f ( x )\) is a polynomial of degree four, having critical points at \(-1,0,1\) . If \(T =\{ x \in R \mid f ( x )= f (0)\},\) then the sum of squares of all the elements of \(T\) is
- A \(6\)
- B \(8\)
- C \(4\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=x(x+1)(x-1)=x^{3}-x\) \(\int d f(x)=\int x^{3}-x d x\) \(f(x)=\frac{x^{4}}{4}-\frac{x^{2}}{2}+C\) \(f(x)=f(0)\) \(x^{2}\left(x^{2}-2\right)=0\) \(x=0,0, \sqrt{2},-\sqrt{2}\) \(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=0+2+2=4\)
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