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
A
$$ - 2 < m < 0$$
B
$$m > 3$$
C
$$ - 1 < m < 3$$
D
$$1 < m < 4$$
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 $$\,\,\, - 1 < m < 3$$
3
AIEEE 2006
MCQ (Single Correct Answer)
If the roots of the quadratic equation $${x^2} + px + q = 0$$ are $$\tan {30^ \circ }$$ and $$\tan {15^ \circ }$$, respectively, then the value of $$2 + q - p$$ is
A
2
B
3
C
0
D
1
Explanation
$${x^2} + px + q = 0$$
Sum of roots $$ = \tan {30^ \circ } + \tan {15^ \circ } = - p$$