The polynomial p(x) = x^2 - (k + 6)x + 2(2k - 1) has the sum of its zeroes equal to half the product of its zeroes. Find the value of k.

Question

Accepted Answer

7. Sum of zeroes = (k + 6). Product = 2(2k - 1). Condition: sum = 1/2(product). So k + 6 = 1/2(4k - 2) = 2k - 1. Then 6 + 1 = 2k - k, so k = 7.

The polynomial $p (x) = x^{2} - (k + 6) x + 2 (2 k - 1)$ has the sum of its zeroes equal to half the product of its zeroes.
Find the value of $k$ .