Question

If $-1$ is one of the roots of the equation $(m-2)x^2+8x+(m+4)=0,$ then $m=$

• A. $3$
• B. $-5$
• C. $-3$

Answer 1

The correct option is A $3$

Given: $(m-2)x^2+8x+(m+4)=0$ and $-1$ is one of the roots of the equation.
Now, we know if $-1$ is of the roots of the equation $a{x}^2+bx+c=0$
$\Rightarrow a-b+c=0\Rightarrow m-2-8+m+4=0\Rightarrow 2m=6\Rightarrow m=3$

2nd Method:
If $-1$ is one of the roots of the equation, then the value of equation at $x=-1$ is $0.$
$(m-2)(-1{)}^2+8(-1)+(m+4)=0$
$\Rightarrow m-2-8+m+4=0\Rightarrow 2m=6\Rightarrow m=3$