Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
6x² + x - 1 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 1 = - 6 and sum = + 1
The factors are - 2 and + 3
Use these factors to split the x- term
6x² - 2x + 3x - 1 = 0 ( factor the first/second and third/fourth terms )
2x(3x - 1) + 1(3x - 1) = 0 ← factor out (3x - 1) from each term
(3x - 1)(2x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]
