Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three real numbers such that $\mathrm{a}+2 \mathrm{~b}+4 \mathrm{c}=0$. Then the equation $\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$

Question

Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three real numbers such that $\mathrm{a}+2 \mathrm{~b}+4 \mathrm{c}=0$. Then the equation $\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$, has both the roots complex, hat its roots lying within $-1 < x < 0$, has one of roots equal to $\frac{1}{2}$, has its roots lying within $2 < x < 6$

MARKS App · Accepted Answer

Hints: $\frac{1}{4} \mathrm{a}+\frac{1}{2} \mathrm{~b}+\mathrm{c}=0$ $\begin{aligned} & \left(\frac{1}{2}\right)^2 a+\left(\frac{1}{2}\right) b+c=0 \ & \therefore x=\frac{1}{2} \end{aligned}$

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