# Find the zeros?

• September 22nd 2009, 01:02 PM
tsmith
Find the zeros?
Find the zeros (if any) of this rational function.
g(x) = (x^3 - 8) / (x^2 + 1)

I'm not sure how to solve this. Any tips?
• September 22nd 2009, 01:09 PM
Plato
What about $x=2?$
• September 22nd 2009, 01:10 PM
tsmith
How did you get that?
• September 22nd 2009, 01:24 PM
Plato
Quote:

Originally Posted by tsmith
How did you get that?

By simple imspection: $2^3-8=0$.
• September 22nd 2009, 06:03 PM
pacman
factoring it we have,

g(x) = (x - 2)(x^2 + 2x + 4)/(x^2 + 1),

@ x = 2; g(x) vanishes ..... this factor (x^2 + 2x + 4) has no real root,

the discriminant is b^2 - 4ac = 2^2 -4(1)(4) = -12 < 0.

The graph below confirms it, x = 2 is the only ZERO of the function
• September 23rd 2009, 05:47 AM
stapel
Quote:

Originally Posted by tsmith
Find the zeros (if any) of this rational function.
g(x) = (x^3 - 8) / (x^2 + 1)

I'm not sure how to solve this. Any tips?

Hint: A fraction is zero when its numerator is zero. (Wink)