JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(f(x)\) is a non-zero polynomial of degree four, having local extreme points at \(x = -1, 0, 1;\) then the set \(S = \{x \in R; f(x) = f(0)\}\) contains exactly
- A four irrational numbers
- B four rational numbers
- C two irrational and one rational number
- D two irrational and two rational numbers
Answer & Solution
Correct Answer
(C) two irrational and one rational number
Step-by-step Solution
Detailed explanation
\({f^\prime }(x) = \lambda (x + 1)(x - 0)(x - 1)\) \( = \lambda \left( {{x^3} - x} \right)\) \(\Rightarrow f(x)=\lambda\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right)+\mu\) Now \(f(x)=f(0)\) \(\Rightarrow \lambda\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right)+\mu=\mu\)…
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