SOLUTION: solve for the zeros or roots of this polynomial equation k(x)= x-(1/x) Please Please explain step by step because I really want to learn how to solve for the zeros of polynom

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve for the zeros or roots of this polynomial equation k(x)= x-(1/x) Please Please explain step by step because I really want to learn how to solve for the zeros of polynom      Log On


   



Question 164559: solve for the zeros or roots of this polynomial equation
k(x)= x-(1/x)
Please Please explain step by step because I really want to learn how to solve for the zeros of polynomial equations. Thank you for any help. Please Help Soon!

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve for the zeros or roots of this polynomial equation
k(x) = x-(1/x)
:
Make the equation = to 0
x - 1%2Fx = 0
:
Multiply equation by x to get rid of the denominator
x*x - x*1%2Fx = x*0
:
results
x^2 - 1 = 0
;
Recognize this as the "difference of square" and can be factored to:
(x+1)*(x-1) = 0; (FOIL this and you will see it)
:
Two solutions
x = -1
and
x = +1
;
;
Prove it to yourself. Substitute -1 for x in the original equation
-1 - 1%2F%28-1%29 = 0
-1 - (-1) = 0
Which is
-1 + 1 = 0
:
Do the same with x=+1