Question

If the roots of the quadratic equation $kx(x+2)+6=0$ are real and equal.then find the value of $k$

Answer 1

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

$\Rightarrow k{x}^2+2kx+6=0$ is quadratic in $x$

Discriminant$\Delta =b^2-4ac$ where $a=k,b=2k$ and $c=6$

Roots are real and equal$\Rightarrow b^2-4ac=0$

$\Rightarrow 4k^2-4\times k\times 6=0$

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

$\Rightarrow k\ne 0,k=6$ if $k=0$, then $0(0+2)+6\ne 0$ from the equation

$\therefore k=6$