The number of distinct real roots of the equation x7 - 7x - 2 = 0 is

Question

Accepted Answer

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

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

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