Question

Determine the maximum number of zeros and the x-intercepts of the function: (x^2-x-2)(3x-2)

Answer 1

Answer:

3

Step-by-step explanation:

note that zeros and x-intercepts are the same with different names

There are 2 zeros from the quadratic factor and 1 from the linear factor.

To find them equate the function to zero, that is

(x² - x - 2)(3x - 2) = 0

(x - 2)(x + 1)(3x-2) = 0 ← factoring the quadratic

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 1 = 0 ⇒ x = - 1

3x - 2 = 0 ⇒ x = $\frac{2}{3}$