Vieta’s Formulas Calculator

This Vieta’s formulas calculator finds the sum and product of the roots of any quadratic straight from its coefficients, without you ever having to solve the equation. Vieta’s formulas connect the coefficients of a polynomial to symmetric functions of its roots: for a quadratic written as ax squared plus bx plus c, the two roots always add to minus b over a, and always multiply to c over a. You enter a, b and c into the three fields, and the calculator instantly returns the sum of the roots, the product of the roots, and the discriminant, b squared minus 4ac. The discriminant is worth watching, because its sign shows what kind of roots you have: positive means two distinct real roots, zero means a single repeated root, and negative means a pair of complex conjugate roots. This makes the tool useful well beyond one calculation. Algebra students can use it to check answers after factorising or applying the quadratic formula by hand, teachers can use it to build examples quickly, and anyone constructing a quadratic with chosen roots can work backwards from a target sum and product to find the coefficients needed. Because Vieta’s whole point is skipping the solving step, this tool works best when you already know a, b and c and just want the relationships confirmed. A worked example and formula are set out below.

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