Question

For what values of k are the roots of the quadratic equation $3x^2+2kx+27=0$ real and equal?

Answer 1

$$\begin{gathered} \text{Given:} \\ \text{3}{x}^2+2kx+27=0 \\ \text{Here,} \\ a=3,b=2k\mathrm{and}c=27 \\ \text{It is given that the roots of the equation are real and equal; therefore, we have:} \\ D=0 \\ \Rightarrow {\left(2k\right)}^2-4\times 3\times 27=0 \\ \Rightarrow 4k^2-324=0 \\ \Rightarrow 4k^2=324 \\ \Rightarrow k^2=81 \\ \Rightarrow k=\pm 9 \\ \therefore k=9\text{or}k=-9 \end{gathered}$$