JEE MAIN - Mathematics (2006 - No. 19)
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 then 4, lie in the interval
$$ - 2 < m < 0$$
$$m > 3$$
$$ - 1 < m < 3$$
$$1 < m < 4$$
Explanation
Equation $${x^2} - 2mx + {m^2} - 1 = 0$$
$${\left( {x - m} \right)^2} - 1 = 0$$
or $$\left( {x - m + 1} \right)\left( {x - m - 1} \right) = 0$$
$$x = m - 1,m + 1$$
$$m - 1 > - 2$$ and $$m + 1 < 4$$
$$ \Rightarrow m > - 1$$ and $$m<3$$
or $$\,\,\, - 1 < m < 3$$
$${\left( {x - m} \right)^2} - 1 = 0$$
or $$\left( {x - m + 1} \right)\left( {x - m - 1} \right) = 0$$
$$x = m - 1,m + 1$$
$$m - 1 > - 2$$ and $$m + 1 < 4$$
$$ \Rightarrow m > - 1$$ and $$m<3$$
or $$\,\,\, - 1 < m < 3$$
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