Question

For what value of $K$ does $(K-12)x^2+2(k-12)x+2=0$ have equal roots.

Answer 1

$(k-12)x^2+2(k-12)x+2=0$

For equal roots $D=0$

$b^2-4ac=0$

$b^2=4ac$

$\Rightarrow {\left[2\right(k-12\left)\right]}^2=4(k-12)\left(2\right)$

$\Rightarrow$$4(k-12{)}^2=8(k-12)$

$\Rightarrow$$k-12=2$

$\therefore k=14$