Question

I’m not sure if my answer correct. If you can please help me.

Answer 1

Two Answers:  -5, 8/3

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Explanation:

We cannot divide by zero.

To figure out when the expression is undefined, set the denominator equal to zero and solve for z.

The quadratic formula is the best route in my opinion.

$6z^2+14z-80 = 0\\\\z = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\z = \frac{-14\pm\sqrt{14^2-4(6)(-80)}}{2(6)}\\\\z = \frac{-14\pm\sqrt{2116}}{12}\\\\z = \frac{-14\pm46}{12}\\\\z = \frac{-14+46}{12} \ \text{ or } \ z = \frac{-14-46}{12}\\\\z = \frac{32}{12} \ \text{ or } \ z = \frac{-60}{12}\\\\z = \frac{8}{3} \ \text{ or } \ z = -5$

Plugging in either z = 8/3 or z = -5 leads to the the denominator 6z^2+14z-80 to be zero. So either of these z values makes the given rational expression to be undefined.