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Question: The maximum number of real roots of the equation \(x^{2n} - 1 = 0\)isB...

The maximum number of real roots of the equation x2n−1=0x^{2n} - 1 = 0isB

A

2

B

3

C

n

D

2n

Answer

2

Explanation

Solution

Let f(x)=x2n−1f(x) = x^{2n} - 1, then f′(x)=x2n−1=0⇒x=0f'(x) = x^{2n - 1} = 0 \Rightarrow x = 0

Sign of f(x)f(x) at x=−∞,0,+∞x = - \infty,0, + \infty are

x: & - \infty & 0 & + \infty \\ f(x): & + ive & - ive & + ive \end{matrix}$$ This show that there are two real roots of $f(x) = 0$ which lie in the interval $( - \infty,0)$ and $(0, + \infty)$. Hence maximum number of real roots are 2.