Question

For how many values of $m$ will the equation $(m+1)x^2+2(m+3)x+(2m+3)=0$ have equal roots?

Answer 1

The given equation is $(m+1)x^2+2(m+3)x+(2m+3)=0$

Here, $a=(m+1),b=2(m+3)$ and $c=(2m+3)$

For equal roots,

$Discriminant=0\Rightarrow b^2-4ac=0$

$\Rightarrow \left[2\right(m+3){]}^2-4(m+1\left)\right(2m+3)=0$

$\Rightarrow \left[\right(m+3){]}^2-(m+1\left)\right(2m+3)=0$

$\Rightarrow m^2+6m+9-2m^2-5m-3=0$

$\Rightarrow -m^2+m+6=0$

$\Rightarrow m^2-m-6=0$

It is a quadratic equation, so m will have two solution

$\therefore$ for $2$ values of m , the equation has equal roots.