Question

Very-Short-Answer Questions

Find the values of k so that the quadratic equation $x^2-4kx+k=0$ has equal roots. [CBSE 2012]

Answer 1

It is given that the quadratic equation $x^2-4kx+k=0$ has equal roots.
$$\begin{gathered} \therefore D=0 \\ \Rightarrow {\left(-4k\right)}^2-4\times 1\times k=0 \\ \Rightarrow 16k^2-4k=0 \\ \Rightarrow 4k\left(4k-1\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow k=0\mathrm{or}4k-1=0 \\ \Rightarrow k=0\mathrm{or}k=\frac{1}{4} \end{gathered}$$

Hence, 0 and $\frac{1}{4}$ are the required values of k.