JEE MAIN - Mathematics (2019 - 12th January Evening Slot - No. 9)
The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x $$ \in $$ R, is always positive, is :
7
8
3
6
Explanation
Expression is always positive it
2m + 1 > 0 $$ \Rightarrow $$ m > $$-$$ $${1 \over 2}$$ &
D < 0 $$ \Rightarrow $$ m2 $$-$$ 6m $$-$$ 3 < 0
3 $$-$$ $$\sqrt {12} $$ < m < 3 + $$\sqrt {12} $$ . . . . (iii)
$$ \therefore $$ Common interval is
3 $$-$$ $$\sqrt {12} $$ < m < 3 + $$\sqrt {12} $$
$$ \therefore $$ Intgral value of m {0, 1, 2, 3, 4, 5, 6}
2m + 1 > 0 $$ \Rightarrow $$ m > $$-$$ $${1 \over 2}$$ &
D < 0 $$ \Rightarrow $$ m2 $$-$$ 6m $$-$$ 3 < 0
3 $$-$$ $$\sqrt {12} $$ < m < 3 + $$\sqrt {12} $$ . . . . (iii)
$$ \therefore $$ Common interval is
3 $$-$$ $$\sqrt {12} $$ < m < 3 + $$\sqrt {12} $$
$$ \therefore $$ Intgral value of m {0, 1, 2, 3, 4, 5, 6}
Comments (0)
