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

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

Here, $a=k-12,b=2(k-12),c=2$

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

$D=4(k-12{)}^2-4(k-12)\times 2$

$D=4(k-12)(k-14)$

The given eqn will have equal roots, if

$D=0$

$4(k-12)(k-14)=0$

$k=12$ or $14$.