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 :
JEE · Math · previous-year question
- A.7correct
- B.8
- C.3
- D.6
Answer
A. 7
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}
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