Question

if alpha , beta are zeroes of polynomial xsquare -(k-6)x + (2k+1) , find K if α+β=αβ​

Answer 1

$\alpha + \beta = \alpha \beta \\ \alpha + \beta = - b \div a = - (k - 6) \\ \alpha \times \beta = c \div a = 2k + 1 \\ compairing \\ - k + 6 = 2k + 1 \\ 3k = 7 \\ k = 7 \div 3 \\ \\ \\ ok \:$

Answer 2

alpha +beta =(k-6)

alpha +beta=(2k+1)

but

it is given that

k-6=2k+1

then

k=-7

I hope it will help you