Use the quadratic formula to solve. Express your answer in simplest form. 2k 2 +11k+12= 0

Answer 1

To solve the quadratic equation 2k^2 + 11k + 12 = 0, we will use the quadratic formula:

k = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 11, and c = 12. Plugging these values into the quadratic formula:

k = (-11 ± √(11^2 - 4*2*12)) / 2*2

k = (-11 ± √(121 - 96)) / 4

k = (-11 ± √25) / 4

k = (-11 ± 5) / 4

Now we have two possible solutions:

1. k = (-11 + 5) / 4
k = -6 / 4
k = -3/2

2. k = (-11 - 5) / 4
k = -16 / 4
k = -4

Therefore, the solutions to the quadratic equation 2k^2 + 11k + 12 = 0 are k = -3/2 and k = -4.