Question

All the value 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. $(-2,0)$
• B. $(3,\infty )$
• C. $(-1,3)$
• D. $(1,4)$

Answer 1

The correct option is C $(-1,3)$

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

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

$(x-m+1)(x-m-1)=0$

$x=m-1,m+1-2<m-1$

and $m+1<4.$

so, $m>-1$ and

$m<3-1m<3$

So, option (c) is correct.