Solve the following equation by factorisation:

$\dfrac{2}{x^2} - \dfrac{5}{x} + 2 = 0, x$ ≠ 0

Given,

$\dfrac{2}{x^2} - \dfrac{5}{x} + 2 = 0 \\[1em] \Rightarrow \dfrac{2 - 5x + 2x^2}{x^2} = 0 \\[1em] \Rightarrow 2 - 5x + 2x^2 = 0 \times x^2 \\[1em] \Rightarrow 2x^2 - 5x + 2 = 0 \\[1em] \Rightarrow 2x^2 - 4x - x + 2 = 0 \\[1em] \Rightarrow2x(x - 2) - 1(x - 2) = 0 \\[1em] \Rightarrow (2x - 1)(x - 2) = 0 \text{ (Factorising left side) } \\[1em] \Rightarrow 2x - 1 = 0 \text{ or } x - 2 = 0 \text{ (Zero-product rule) } \\[1em] \Rightarrow 2x = 1 \text{ or } x = 2 \\[1em] x = \dfrac{1}{2} \text{ or } x = 2 \\[1em]$

Hence, the roots of given equation are $\dfrac{1}{2}$ , 2.