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<5
• C. 1<m<3
• D. -1<m<5

Answer 1

The correct option is A

-1<m<3

If roots $a{x}^2+bx+c=0$ lie between $k_1$ and $k_2$ then of $\left(k_1\right)$ > 0, of $\left(k_2\right)$ > 0 and $k_1$ < $\frac{-b}{2a}$ < $k_2$
f(-2)>0, f(4) > 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]