Question

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

• A. 5
• B. 7
• C. 1
• D. 3

Answer 1

Answer: (D)

$x^7-7x-2=0$
$x^7-7x=2$
$f(x)=x^7-7x(\text{ odd })\&y=2$
$f(x)=x\left(x^2-7^{1/3}\right)\left(x^4+x^2\cdot 7^{1/3}+7^{2/3}\right)$
$f^{\prime }(x)=0$
$\Rightarrow x=\pm 1$