Question

The values of k for which the quadratic equation x² – 4kx + k = 0 has equal roots, are _________.

Answer 1

Let x² – 4kx + k = 0 be a quadratic equation.

It is given that, it has equal roots.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}=0 \\ \Rightarrow b^2-4ac=0 \\ \Rightarrow {\left(-4k\right)}^2-4\left(1\right)\left(k\right)=0 \\ \Rightarrow 16k^2-4k=0 \\ \Rightarrow 4k\left(4k-1\right)=0 \\ \Rightarrow 4k=0\mathrm{or}4k-1=0 \\ \Rightarrow k=0\mathrm{or}k=\frac{1}{4} \end{gathered}$$

Hence, the values of k for which the quadratic equation x² – 4kx + k = 0 has equal roots, are $\underline{0\mathrm{or}\frac{1}{4}}$ .