1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of distinct real roots of the equation x7-7 x-2=0 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The number of distinct real roots of the equation $x^{7}-7 x-2=0$ is

JEE MainJEE Main 2022Application of Derivatives

Solution:

$x^{7}-7 x-2=0$
$x^{7}-7 x=2$
$f(x)=x^{7}-7 x$ (odd) & $y=2$
$f(x)=x\left(x^{2}-7^{1 / 3}\right)\left(x^{4}+x^{2} \cdot 7^{1 / 3}+7^{2 / 3}\right)$
$f^{\prime}(x)=7\left(x^{6}-1\right)=7\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)$
$f^{\prime}(x)=0 \Rightarrow x=\pm 1$
image
$f(x) = 2$ has $3$ real distinct solution.