Question

Solve each of the following quadratic equations:

$100x^2-20x+1=0$

Answer 1

We write, $-20x=-10x-10x$ as $100x^2\times 1=100x^2=\left(-10x\right)\times \left(-10x\right)$
$$\begin{gathered} \therefore 100x^2-20x+1=0 \\ \Rightarrow 100x^2-10x-10x+1=0 \\ \Rightarrow 10x\left(10x-1\right)-1\left(10x-1\right)=0 \\ \Rightarrow \left(10x-1\right)\left(10x-1\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow {\left(10x-1\right)}^2=0 \\ \Rightarrow 10x-1=0 \\ \Rightarrow x=\frac{1}{10} \end{gathered}$$
Hence, $\frac{1}{10}$ is the repreated root of the given equation.