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alpha +beta=-b/a
alpha+beta=-(-k-6)
alpha+beta=k+6
alpha*beta=c/a
alpha*beta==4k-2
now put these values in the equation
alpha+beta=alpha*beta/2
k+6=4k-2/2
k+6=2(2k-1)/2
k+6=2k-1
k-2k=-1-6
-k=-7
k=7
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