Find the values of k in the equation 6k2 = 5k + 6
A
{\(\frac{-2}{3}, \frac{-3}{2}\)}
B
{\(\frac{-2}{3}, \frac{3}{2}\)}
C
{\(\frac{2}{3}, \frac{-3}{2}\)}
D
{\(\frac{2}{3}, \frac{3}{2}\)}
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
6k2 = 5k + 6
6k2 - 5k - 6 = 0
6k2 - 0k + 4k - 6 = 0
3k(2k - 3) + 2(2k - 3) = 0
(3k + 2)(2k - 3) = 0
3k + 2 = 0 or 2k - 3 = 0
3k = -2 or 2k = 3
k = \(\frac{-2}{3}\) or k = \(\frac{3}{2}\)
k = (\(\frac{-2}{3}\), k = \(\frac{3}{2}\))
Source: Myschool Past Questions Archive (Record #36884)