F(x)= \frac{X^2-x-12} {5x^2+4x} Find all x-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of x…

Question

`f(x)= \frac{X^2-x-12} {5x^2+4x}`

Find all x-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of x-intercepts.

Answer 1

(- 3, 0 ), (4, 0 )

Explanation:

To find the x- intercepts let f(x) = 0

`(x^2-x-12)/(5x^2+ 4x)` = 0

The denominator cannot equal zero as this would make f(x) undefined.

Equate the numerator to zero and solve for x

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

x- intercepts are (- 3, 0 ) and (4, 0 )