Question

Find the values of $k$ for which the following equation has equal roots
$(k-12)x^2+2(k-12)x+2=0$

Answer 1

Condition for quadratic equation to have equal roots is

$b^2-4ac=0$

Given,

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

we have,

$a=(k-12)$

$b=2(k-12)$

$c=2$

$\Rightarrow \left[2\right(k-12){]}^2-4[(k-12)\left(2\right)]=0$

$\left[4\right(k^2+144-24k\left)\right]-8(k-12)=0$

$4k^2-104k+672=0$

$(k-14)(k-12)=0$

$\therefore k=14,12$