Question

For What value of $K,X=\alpha$ is a solution of equation $x^2-(a+b)x+k=0$

Answer 1

If $x=\alpha$ is solution os

$x^2-(a+b)x+k=0$ ________ (1)

then $x=\alpha$ satisfies equation (1) so

we get,

${\alpha }^2-(a+b)\alpha \ne k=0$

$k=\alpha [a+b-\alpha ]$

Hence value of k is $[a+b-\alpha ]$