Question

The value of $k$ for which the roots are real and equal of the following equations
$kx(x-2)+6=0$ is ____

Answer 1

$kx(x-2)+6=0$

$\Rightarrow$ $k{x}^2-2kx+6=0$

$\Rightarrow$ Here, $a=k,b=-2k,c=6$

$\Rightarrow$ It is given that rots are real and equal.

$\therefore$ $b^2-4ac=0$

$\Rightarrow$ $(-2k{)}^2-4(k\left)\right(6)=0$

$\Rightarrow$ $4k^2-24k=0$

$\Rightarrow$ $4k(k-6)=0$

$\Rightarrow$ $4k=0$ and $k-6=0$

$\therefore$ $k=0$ and $k=6$

$\therefore$ The value of $k$ is $6$.