If the roots of the equation $3 x^2+4 k x+3=0$ are non-real, then $\mathrm{k}$ lies in the interval

Question

Aicharya · Accepted Answer

Given: $3 \mathrm{x}^2+4 \mathrm{kx}+3=0$ Above eq ${ }^{\mathrm{n}}$ has non-real roots if $ \begin{aligned} & (4 \mathrm{k})^2-4 	imes 3 	imes 3 < 0 \ & \Rightarrow 16 \mathrm{k}^2-36 < 0 \ & \Rightarrow \mathrm{k}^2 < \frac{9}{4} \ & \Rightarrow-\frac{3}{2} < \mathrm{k} < \frac{3}{2} \end{aligned} $ $\Rightarrow \mathrm{k}$ lies in the interval $\left(-\frac{3}{2}, \frac{3}{2}ight)$

If the roots of the equation $3 x^2+4 k x+3=0$ are non-real, then $\mathrm{k}$ lies in the interval

Solution