New quadratic formula

This paper introduces a novel alternative expression for solving quadratic equations, derived through the manipulation of Vieta’s formulas. Traditionally, the roots of a quadratic equation ax² + bx + c = 0 are given by the quadratic formula. However, by expressing the roots (α and β) in terms of their sum and product, α + β = -b/a and αβ = c/a, we derive a complementary expression: β = 2c / (-b ± √(b² - 4ac)), which functions as a counterpart to the classic root formula for α, that is, α = (-b±√(b²-4ac))/2a. This derivation not only reinforces the relationship between Vieta’s formulas and the standard quadratic formula but also offers an alternative perspective on root computation. Through examples, we demonstrate the validity of this expression and its potential utility in algebraic problem-solving.