The number of integral values of m for which | vedclass

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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 - \sq

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$7$

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Expression is always positive it $2 \mathrm{m}+1>0 \Rightarrow \mathrm{m}>-\frac{1}{2}$ and $D<0 \Rightarrow m^{2}-6 m-3<0$ $3 - \sqrt {12} < m < 3 + \sqrt {12} ..........(iii)$ $ herefore$ Common interval is $3-\sqrt{12}<\mathrm{m}<3+\sqrt{12}$ $ herefore $ Integral value of $\mathrm{m}\{0,1,2,3,4,5,6\}$

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

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