Question

Very-Short-Answer Questions

Find the values of k for which the quadratic equation $9x^2-3kx+k=0$ has equal roots. [CBSE 2014]

Answer 1

It is given that the quadratic equation $9x^2-3kx+k=0$ has equal roots.
$$\begin{gathered} \therefore D=0 \\ \Rightarrow {\left(-3k\right)}^2-4\times 9\times k=0 \\ \Rightarrow 9k^2-36k=0 \\ \Rightarrow 9k\left(k-4\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow k=0\mathrm{or}k-4=0 \\ \Rightarrow k=0\mathrm{or}k=4 \end{gathered}$$

Hence, 0 and 4 are the required values of k.