Question

The value(s) of $m$ such that the roots of the quadratic equation $(m+1)x^2+(m+1)x-m+1=0$ are equal is

• A. $-\frac{3}{5}$
• B. $1$
• C. $\frac{3}{5}$
• D. $-1,\frac{3}{5}$

Answer 1

The correct option is C $\frac{3}{5}$

$(m+1)x^2+(m+1)x-(m-1)=0$
For the given equation to be quadratic
$m+1\ne 0\Rightarrow m\ne -1$
The roots are equal, so
$D=0$
$\Rightarrow (m+1{)}^2+4(m+1\left)\right(m-1)=0\Rightarrow (m+1\left)\right(m+1+4m-4)=0\Rightarrow (m+1\left)\right(5m-3)=0\therefore m=\frac{3}{5}(\because m+1\ne 0)$