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?
Answer: -24
Explanation
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
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