Question

All the values of $m$ for which both roots of the equation $x^2+2mx+m^2-1=0$ are greater than $-2$ but less than $4$ lie in the interval

• A. $-2<m<0$
• B. $m>3$
• C. $-1<m<3$
• D. $1<m<4$

Answer 1

The correct option is C $-1<m<3$

Given equation $x^2-2mx+m^2-1=0$

$\Rightarrow {(x-m)}^2-1=0\Rightarrow (x-m-1)(x-m+1)=0$

$\Rightarrow x=m-1,m+1\Rightarrow -2<m-1$ and $m+1<4$

$m>-1$ and $m<3$ $\Rightarrow -1<m<3$