Question

sum of the roots of a quadratic equation is double their product . find k if equation is x²-4kx+3=0

Answer 1

Answer
It's right now, but I think I do not

Answer 2

comparing with
$a {x}^{2} + bx + c = 0$
a=1 b=-4 c= k+3
$\alpha \: and \: \beta \: are \: the \: roots \: of \: given \: equatin$
from given condition
$\alpha + \beta = 2( \alpha \times \beta ).....1$
$\alpha + \beta = \frac{ - b }{a}$
$\frac{ - ( - 4k)}{1}$
$\alpha + \beta = 4k.......2$
$\alpha \times \beta = \frac{c}{a}$
$\frac{k + 3}{1}$
$\alpha \times \beta = k + 3.......3$
from equation 1 2 and 3
$\alpha + \beta = 2( \alpha \times \beta )$
$4k = 2(k + 3) \\ 4k = 2k + 6 \\ 4k - 2k = 6 \\ 2k = 6 \\ k = \frac{6}{3 } \\ k = 2$