A NEW WAY OF SOLVING QUADRATIC EQUATIONS : The Quadratic Method

The Quadratic Triangle is a heuristic visualization for estimating quadratic roots. At its apex lies the pivot p=S/mp = S/mp=S/m, derived from dividing the sum of roots SSS. Using this pivot, one root is approximated as r1=P/pr_1 = P/pr1=P/p, and the other as r2=S−r1r_2 = S - r_1r2=S−r1. A ceiling adjustment refines both values to align with integer or near-integer solutions. The triangular form highlights the balance between coefficients, sum, product, and the approximated roots.