Answer:
The roots are {-1/2, 5/3}.
Step-by-step explanation:
6x^2 - 7x - 5 = 0
Use the 'ac' method:
6 * -5 = -30 so we need to find 2 values whose product is -30 and whose sum = the coefficient of x in the given equation ( -7).
-10 and + 3 fit the bill so we write:
6x^2 - 7x - 5 = 0
6x^2 + 3x - 10x - 5 = 0 Factor by grouping:
3x(2x + 1) - 5(2x + 1) = 0
(3x - 5)(2x + 1) = 0
So 3x - 5 = 0 gives x = 5/3, and
2x + 1 = 0 gives x = -1/2.
