Question

If α and β are zeroes of the quadratic polynomial p(x)= x^2 - (k+6)x +2(2k-1) then find the value of k if α+β=αβ/2

Answer 1

if
α,β are roots then α+β = -b/a
αβ = c/a

α+β = αβ/2
-b/a = c/a/2
-b/a = c/2a
-b = c/2
--(k+6) = 2(2k-1)/2
k+6 = 2k-1
6+1 = 2k-k
k = 7

Answer 2

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