Question

sum of the roots of a quadratic equation is double their product. find k if equation is $x^2-4kx+k+3=0$

Answer 1

$x^2-4kx+k+3=0$

$\alpha +\beta =4k$

$\alpha \beta =(k+3)$

$\alpha +\beta =2\alpha \beta$

$\Rightarrow 4k=2(k+3)$

$\Rightarrow 4k=2k+6$

$\Rightarrow 2k=6$

$\Rightarrow k=3$.