Find the value of k so that the sum of the roots of the equation 2x² + kx + 6 = 0 is equal to four times the product of its roots?

-24

-22

-18

None of these

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Given the equation 2x² + kx + 6 = 0, we have:

Sum of the roots = -k/2

Product of the roots = 6/2 = 3

According to the problem, the sum of the roots is equal to four times the product of the roots:

-k/2 = 4 * 3

-k/2 = 12

k = -24