Question

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. 8
• B. 7
• C. 6
• D. 3

Answer 1

Answer: (B)

Exprsssion is always positve it
$2m+1>0\Rightarrow m>-\frac{1}{2}$
&
$D<0\Rightarrow m^2-6m-3<0$
$3-\sqrt{12}<m<3+\sqrt{12}...(iii)$
$\therefore$Common interval is
$3-\sqrt{1}<m<3+\sqrt{12}$
$\therefore$Integral value of m {0,1,2,3,4,5,6}