Answer:
B
Step-by-step explanation:
Given
12x² - 3x - 9 = 0 ( divide all terms by 3 )
4x² - x - 3 = 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 = 4 × - 3 = - 12 and sum = - 1
The factors are - 4 and + 3
Use these factors to split the x- term
4x² - 4x + 3x - 3 = 0 ( factor the fist/second and third/fourth terms )
4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(4x + 3) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
4x + 3 = 0 ⇒ 4x = - 3 ⇒ x = - [tex]\frac{3}{4}[/tex]
