Answer:
x = - 1, x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
3x² + 2x - 1 ( to find the zeros, equate to zero )
3x² + 2x - 1 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 1 = - 3 and sum = + 2
The factors are + 3 and - 1
Use these factors to split the x- term
3x² + 3x - x - 1 = 0 ( factor first/second and third/fourth terms )
3x(x + 1) - 1 (x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(3x - 1) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]
