Find all x-intercepts of the function.
-$$f ( x ) = x ^ { - 2 } + x ^ { - 1 } - 30$$
A)(6, 0), (-5, 0)
B) $$\left( \frac { 1 } { 6 } , 0 \right) , \left( - \frac { 1 } { 5 } , 0 \right)$$
C)(-6, 0), (5, 0)
D) $$\left( - \frac { 1 } { 6 } , 0 \right) , \left( \frac { 1 } { 5 } , 0 \right)$$

Question

Quizplus · Accepted Answer

The x-intercepts are the points where the function equals zero. So, we need to solve the equation f(x) = 0.$$x ^ { - 2 } + x ^ { - 1 } - 30 = 0$$$$x ^ { - 2 } + x ^ { - 1 } = 30$$$$\frac { 1 } { x ^ { 2 } } + \frac { 1 } { x } = 30$$$$\frac { 1 + x } { x ^ { 2 } } = 30$$$$1 + x = 30x ^ { 2 }$$$$30x ^ { 2 } - x - 1 = 0$$$$(6x + 1)(5x - 1) = 0$$$$x = - \frac { 1 } { 6 } , \frac { 1 } { 5 }$$So, the x-intercepts are $$\left( - \frac { 1 } { 6 } , 0 \right) , \left( \frac { 1 } { 5 } , 0 \right)$$

Find All X-Intercepts of the Function f(x)=x−2+x−1−30f ( x ) = x ^ { - 2 } + x ^ { - 1 } - 30f(x)=x−2+x−1−30

Find All X-Intercepts of the Function $f ( x ) = x ^ { - 2 } + x ^ { - 1 } - 30$