The number of integral values of

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 :

 

  1. 8

  2. 7

  3. 6

  4. 3


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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