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?

Printable View

- Sep 22nd 2009, 01:02 PMtsmithFind 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? - Sep 22nd 2009, 01:09 PMPlato
What about $\displaystyle x=2?$

- Sep 22nd 2009, 01:10 PMtsmith
How did you get that?

- Sep 22nd 2009, 01:24 PMPlato
- Sep 22nd 2009, 06:03 PMpacman
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 - Sep 23rd 2009, 05:47 AMstapel