Solve the following equation by factorisation:

x² - (p + q)x + pq = 0

Given,

$x^2 - (p + q)x + pq = 0\\[0.5em] \Rightarrow x^2 - px - qx + pq = 0 \\[0.5em] \Rightarrow x(x - p) - q(x - p) = 0 \\[0.5em] \Rightarrow (x - q)(x - p) = 0 \text{ (Factorising left side) }\\[0.5em] \Rightarrow x -q = 0 \text{ or } x - p = 0 \text{ (Zero-product rule)}\\[0.5em] \Rightarrow x = q \text{ or } x = p. \\[0.5em]$

Hence, the roots of given equation are p, q.