# For what values of #k# will the function #f(x) = (x^2-1)/(x-k)^2# have a zero?

##### 1 Answer

Aug 7, 2017

Regardless of the value of

#### Explanation:

Given:

#f(x) = (x^2-1)/(x-k)^2#

For any given value of

The numerator can be factored as a difference of squares:

#x^2-1 = x^2-1^2 = (x-1)(x+1)#

This takes the value

Hence we have three cases:

#k = 1#

in which case#f(-1) = 0#

#k = -1#

in which case#f(1) = 0#

#k != 1# and#k != -1#

in which case both#f(-1) = 0# and#f(1) = 0#