Question

What are the solutions of the equation 3x² + 6x − 24 = 0 ?

A. −2, 4
B. 2, −4
C. 4, −6
D. −4, 6

Answer 1

The solutions to the equation 3x² + 6x − 24 = 0 are found by factoring the simplified form x² + 2x − 8 to get (x + 4)(x − 2) and setting each factor to zero to find x = − 4 and x = 2.

Step-by-step explanation:

The solutions to the equation 3x² + 6x − 24 = 0 are found by factoring the simplified form x² + 2x − 8 to get (x + 4)(x − 2) and setting each factor to zero to find x = − 4 and x = 2.

The solutions to the equation 3x² + 6x − 24 = 0 can be found by either factoring the quadratic equation or using the quadratic formula. Let's try to factor first:

1. Divide all terms by 3 to simplify the equation: x² + 2x − 8 = 0.
2. Now we look for two numbers that multiply to − 8 and add to 2. These numbers are 4 and − 2.
3. Thus the factors are: (x + 4)(x − 2) = 0.
4. Setting each factor equal to zero gives us: x + 4 = 0 or x − 2 = 0.
5. Therefore, the solutions are x = − 4 and x = 2.

Answer choice B, which is 2 and − 4, is the correct set of solutions of the equation 3x² + 6x − 24 = 0.