help please!!4

Question

Show how to use factoring to find the x intercept of y=3x^2 -19x- 14. identify the roots after you have factored.

Answer 1

y = 3x² - 19x - 14

Now factorize right hand side of above equation.

Multiply first term 3x² and last term - 14 = - 42x²

The correct pair of the terms - 21x and 2x multiply to - 42x² and add to - 19x.

Replace the middle term - 19x with - 21x + 2x.

y = 3x² - 21x + 2x - 14

Group the terms into two pairs.

y = (3x² - 21x) + (2x - 14)

Factor out 3x from the first group  and factor out 2 from the second group.

y = 3x(x - 7) + 2(x - 7)

Factor out common term x - 7.

y = (x - 7)(3x + 2)

Roots of the equation x = 7 and x = - 2/3.

To find x intercepts substitute y = 0 in above equation.

(x - 7)(3x + 2) = 0

Apply zero product property.

x - 7= 0 and 3x + 2 = 0

x = 7 and x = - 2/3

x intercepts are 7 and -2/3.