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4-2.Quadratic Equations and Inequations
hard
The number of integral values of $m$ for which the quadratic expression, $(1 + 2m)x^2 -2(1+ 3m)x + 4(1 + m),$ $x\in R,$ is always positive, is
A
$3$
B
$8$
C
$7$
D
$6$
(JEE MAIN-2019)
Solution
Expression is always positive it $2 \mathrm{m}+1>0 \Rightarrow \mathrm{m}>-\frac{1}{2}$
and $D<0 \Rightarrow m^{2}-6 m-3<0$
$3 – \sqrt {12} < m < 3 + \sqrt {12} ……….(iii)$
$\therefore$ Common interval is $3-\sqrt{12}<\mathrm{m}<3+\sqrt{12}$
$\therefore $ Integral value of $\mathrm{m}\{0,1,2,3,4,5,6\}$
Standard 11
Mathematics
