Question

All the values of $m$ for which both the 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 $-1<m<3$

The given equation is
$x^2-2mx+m^2-1=0$
or $(x-m{)}^2-1=0$
or $(x-m+1)(x-m-1)=0$
or $x=m-1,m+1$
From given condition,
$m-1>-2$ and $m+1<4$
$\Rightarrow m>-1$ and $m<3$
Hence, $-1<m<3$.