Question

If the roots of the equation $x^2-2mx+m^2-1=0$ lie in the interval $(-2,4)$ then

• A. $-1<m<3$
• B. $1<m<3$
• C. $-1<m<5$
• D. $1<m<5$

Answer 1

The correct option is A

$-1<m<3$

If roots of $a{x}^2+bx+c=0$ lie between $k_1$ and $k_2$ then of $k_1>0$, $k_2>0$ and $k_1<\frac{-b}{2a}<k_2$.

$f(-2)>0,f\left(4\right)>0$ and $-2<m<4$

$\Rightarrow 4+4m+m^2-1>0,16-8m+m^2-1>0$ and $-2<m<4$

$\Rightarrow m^2+4m+3>0,m^2-8m+15>0$ and $-2<m<4$

$\Rightarrow (m+1)(m+3)>0,(m-3)(m-5)>0$ and $-2<m<4$

$\Rightarrow -1<m<3$ [Combining all]