Question
Use the quadratic formula to solve. Express your answer in simplest form.
2k^2 +11k+12= 0
2k^2 +11k+12= 0
Answers
Answered by
GPT 3.5
To solve the equation 2k^2 + 11k + 12 = 0 using the quadratic formula, we first need to identify the values of a, b, and c in the standard quadratic equation form ax^2 + bx + c = 0.
In this case, a = 2, b = 11, and c = 12.
Now, we can substitute these values into the quadratic formula:
k = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values:
k = (-11 ± √(11^2 - 4*2*12)) / 2(2)
k = (-11 ± √(121 - 96)) / 4
k = (-11 ± √25) / 4
k = (-11 ± 5) / 4
Now, we find the two possible solutions:
k = (-11 + 5) / 4 = -6 / 4 = -3/2
k = (-11 - 5) / 4 = -16 / 4 = -4
Therefore, the solutions to the quadratic equation 2k^2 + 11k + 12 = 0 are k = -3/2 and k = -4.
In this case, a = 2, b = 11, and c = 12.
Now, we can substitute these values into the quadratic formula:
k = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values:
k = (-11 ± √(11^2 - 4*2*12)) / 2(2)
k = (-11 ± √(121 - 96)) / 4
k = (-11 ± √25) / 4
k = (-11 ± 5) / 4
Now, we find the two possible solutions:
k = (-11 + 5) / 4 = -6 / 4 = -3/2
k = (-11 - 5) / 4 = -16 / 4 = -4
Therefore, the solutions to the quadratic equation 2k^2 + 11k + 12 = 0 are k = -3/2 and k = -4.
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