Question

If both the roots of the equation $4x^2-2x+m=0$ lie in the interval $\left(-1,1\right)$ , then

• A. $-3<m<-2$
• B. $0<m<2$
• C. $2<m<\frac{5}{2}$
• D. $-2<m\le \frac{1}{4}$

Answer 1

Answer: (D)

Coefficient of $x^2$ is positive
So, $D\ge 0,f\left(1\right)>0,f\left(-1\right)>0$
$D\ge 0\Rightarrow 4-4\times 4\times m\ge 0\Rightarrow m\le \frac{1}{4}$
$f\left(-1\right)>0\Rightarrow 4+2+m>0\Rightarrow m>-6$
$f\left(1\right)>0\Rightarrow 4-2+m>0\Rightarrow m>-2$
Taking intersection we get $m\in \left(-2,\frac{1}{4}\right]$