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. $-2 < m\leq \frac{1}{4}$

Answer 1

Answer: (D)

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