QJEEM22Ma7ff7: JEE Main 2022 Mathematics - Class 11 JEEM22Ma7ff7 Solution: The number of distinct real roots of the equation x 7 − 7x − 2…

Question

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The number of distinct real roots of the equation

x⁷ $-$ 7x $-$ 2 = 0 is

Accepted Answer

Given equation $x^{7} - 7 x - 2 = 0$

Let $f (x) = x^{7} - 7 x - 2$

$f^{'} (x) = 7 x^{6} - 7 = 7 (x^{6} - 1)$

and $f^{'} (x) = 0 \Rightarrow x = + 1$

and $f (- 1) = - 1 + 7 - 2 = 5 > 0$

$f (1) = 1 - 7 - 2 = - 8 < 0$

So, roughly sketch of f(x) will be

JEE Main 2022 (Online) 24th June Evening Shift Mathematics - Quadratic Equation and Inequalities Question 63 English Explanation

So, number of real roots of f(x) = 0 and 3

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