Question

If $x=\frac{-1}{2}$ is a root of the quadratic equation 3x² + 2kx + 3 = 0, find the values of k.

Answer 1

Since, $x=\frac{-1}{2}$ is a root of the quadratic equation 3x² + 2kx + 3 = 0,
then, it must satisfies the equation.

$$\begin{gathered} 3{\left(-\frac{1}{2}\right)}^2+2k\left(-\frac{1}{2}\right)+3=0 \\ \Rightarrow 3\left(\frac{1}{4}\right)-k+3=0 \\ \Rightarrow \frac{3}{4}-k+3=0 \\ \Rightarrow \frac{3-4k+12}{4}=0 \\ \Rightarrow 3-4k+12=0 \\ \Rightarrow 4k=15 \\ \Rightarrow k=\frac{15}{4} \\ \mathrm{Hence},\mathrm{the}\mathrm{value}\mathrm{of}k\mathrm{is}\frac{15}{4}. \end{gathered}$$