Zeroing out

Algebra Level 2

Let x be a real number.

Consider the function x 2 − 1 ( x 2 + 1 ) 2 \dfrac{x^2 - 1}{\left(x^2 + 1\right)^2}

How many zeroes does it have?

3 2 0 4 1

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Feb 2, 2016

The denominator is always positive, so it has no singularities. It has zeros where the numerator is zero.

x 2 − 1 = 0 x^2 - 1 = 0

x 2 = 1 x^2 = 1

x =1 or x = -1. That is two zeros.

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Moderator note:

Simple standard approach.

Oh! You meant root I thought of the number 0.

Department 8 - 5 years, 4 months ago

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The zeros of a function f ( x ) f(x) are the roots to the equation f ( x ) = 0 f(x) =0 .

Calvin Lin Staff - 5 years, 3 months ago

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I know but I was confused as I will listening to songs.

Department 8 - 5 years, 3 months ago

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