Question

If 3x² – 11x – 4 = (3x + 1)(x – 4), which equations should be solved to find the roots of 3x² – 11x – 4 = 0? Check all that apply.

a. x + 4 = 0
b. 3x + 1 = x – 4
c. 3x + 1 = 0
d. x – 4 = 0
e. 3x – 1 = 0

Answer 1

To find the roots of the equation 3x² – 11x – 4 = 0, set the equation equal to zero and solve for x by setting each factor equal to zero. The roots of the equation are x = -1/3 and x = 4.

Step-by-step explanation:

To find the roots of the equation 3x² – 11x – 4 = 0, we need to set the equation equal to zero and solve for x. The equation is already factored as (3x + 1)(x – 4), so we can set each factor equal to zero and solve for x:

• (3x + 1) = 0: Solving this equation gives x = -1/3
• (x – 4) = 0: Solving this equation gives x = 4

So, the roots of the equation are x = -1/3 and x = 4. Therefore, options c and d should be solved to find the roots of the equation.