JEE PYQ: Application Of Derivatives Question 60
Question 60 - 2019 (09 Apr Shift 1)
If $f(x)$ is a non-zero polynomial of degree four, having local extreme points at $x = -1, 0, 1$; then the set $S = {x \in \mathbb{R} : f(x) = f(0)}$ contains exactly:
(1) four irrational numbers
(2) four rational numbers
(3) two irrational and two rational numbers
(4) two irrational and one rational number
Show Answer
Answer: (4)
Solution
$f’(x) = kx(x+1)(x-1)$. $f(x) = k(\frac{x^4}{4} - \frac{x^2}{2}) + f(0)$. $f(x) = f(0) \Rightarrow x^2(\frac{x^2}{2} - 1) = 0$: $x = 0, \pm\sqrt{2}$. So $S = {0, -\sqrt{2}, \sqrt{2}}$: two irrational and one rational.
BETA
