Question

The values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots are ______.

Answer 1

Let 2x² – kx + k = 0 be a quadratic equation.

It is given that, it has equal roots.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}=0 \\ \Rightarrow b^2-4ac=0 \\ \Rightarrow {\left(-k\right)}^2-4\left(2\right)\left(k\right)=0 \\ \Rightarrow k^2-8k=0 \\ \Rightarrow k\left(k-8\right)=0 \\ \Rightarrow k=0,8 \end{gathered}$$

Hence, the values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots are 0 or 8.