Find the value of k such that the polynomial x^2-(k+6)x+2(2k-1) has sum of its zeros equal to half of their product.

Let the roots beα,βFor a quadratic equationax2+bx+c=0Sum of rootsα+β=k+6⋯(1)Product of rootsαβ=4k𕒶⋯(2)According to question,α+β=αβ2From(1),(2)⟹k+6=2k𕒵⟹k=7