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 which of the following intervals?

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

Answer 1

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

The given equation is,

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

$\Rightarrow$ $x^2-2mx+m^2=1$

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

$\Rightarrow$ $x-m=1$ or $x-m=-1$

$\Rightarrow$ $x=m+1,m-1$

The roots are $(m+1)$ and $(m-1)$

As per question,

$\Rightarrow$ $-2<m+1<4$

$\Rightarrow$ $-3<m<3$ ----- ( 1 )

And

$\Rightarrow$ $-2<m-1<4$

$\Rightarrow$ $-1<m<5$ ---- ( 2 )

From ( 1 ) and ( 2 ) the value $m$ satisfying the given condition is $-1<m<3$