If a quadratic equation can be factorised, the factors can be used to find the roots of the equation. The equation factorises to give \((x + 3) (x - 2) = 0 \) so the solutions to the equation \(x^2 + ...

We derive midpoint criteria for solving Pell's equation x² - Dy² = ±1, using the nearest square continued fraction expansion of $\sqrt D $ . The period of the expansion is on average 70% that of the ...