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)

3

Answer 2

Given equation $x^7 – 7x – 2 = 0$

Let $f(x) = x^7 – 7x – 2$

$f′(x) = 7x^6 – 7 = 7(x^6 – 1)$

and $f′(x) = 0 ⇒ x = +1$

and $f(–1) = –1 + 7 – 2 = 5 > 0$

$f(1) = 1 – 7 – 2 = –8 < 0$

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

Hence, the correct option is (D): $3$