JEE MAIN - Mathematics (2022 - 24th June Evening Shift - No. 10)

The number of distinct real roots of the equation

x⁷ $$-$$ 7x $$-$$ 2 = 0 is

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

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

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

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