Answer:
see explanation
Explanation:
given
f(x) =3x² - x - 4
To obtain roots set f(x) = 0, that is
3x² - x - 4 = 0
To factor 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 × - 4 = - 12 and sum = - 1
The factors are + 3 and - 4
Use these factors to split the x- term
3x² + 3x - 4x - 4 = 0 ( factor the first/second and third/fourth terms )
3x(x + 1) - 4(x + 1) = 0 ← factor out (x + 1)
(x + 1)(3x - 4) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x - 4 = 0 ⇒ 3x = 4 ⇒ x =
The roots are x = - 1 and x =
By the list provided that would give option 1