Question:
Very-Short-Answer Questions
Find the values of $k$ so that the quadratic equation $x^{2}-4 k x+k=0$ has equal roots.
Solution:
It is given that the quadratic equation $x^{2}-4 k x+k=0$ has equal roots.
$\therefore D=0$
$\Rightarrow(-4 k)^{2}-4 \times 1 \times k=0$
$\Rightarrow 16 k^{2}-4 k=0$
$\Rightarrow 4 k(4 k-1)=0$
$\Rightarrow k=0$ or $4 k-1=0$
$\Rightarrow k=0$ or $k=\frac{1}{4}$
Hence, 0 and $\frac{1}{4}$ are the required values of $k$.