Question:
The number of integral values of $m$ for which the quadratic expression.
$(1+2 m) x^{2}-2(1+3 m) x+4(1+m), x \in R$, is
always positive, is :
Correct Option: , 2
Solution:
Exprsssion is always positve it
$2 m+1>0 \Rightarrow m>-\frac{1}{2}$
$\&$
$\mathrm{D}<0 \Rightarrow \mathrm{m}^{2}-6 \mathrm{~m}-3<0$
$3-\sqrt{12}<\mathrm{m}<3+\sqrt{12}$ ......(iii)
$\therefore$ Common interval is
$3-\sqrt{12}<\mathrm{m}<3+\sqrt{12}$
$\therefore$ Intgral value of $\mathrm{m}\{0,1,2,3,4,5,6\}$
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