Quadratic Plus Root Calculator

Formula

Positive branch root = (-b+sqrt(b × b-4 × a × c)) ÷ (2 × a)

Worked example

With a: 1, b: -3, c: 2, positive branch root is 2.

Calculation method

The rule is Positive branch root = (-b+sqrt(b × b-4 × a × c)) ÷ (2 × a).

Reading positive branch root

The discriminant b² − 4ac controls the number of real roots. The plus and minus branches can return two different roots. In the worked values on this page, a 1, b -3, c 2 produce positive branch root 2.

Practical use

Use the calculation to solve or check a quadratic equation from known coefficients. The specific task here is to find positive branch root from a, b, c.

Limits and common mistakes

The coefficient a must be nonzero. A negative discriminant has no real roots, though complex roots exist outside this real-number tool. Verify a before interpreting positive branch root; a value measured on another basis would answer a different question.

Why the relationship works

For ax² + bx + c = 0, the discriminant b² − 4ac determines whether real roots can be calculated. A positive value gives two distinct real roots, zero gives a repeated root, and a negative value gives no real root. The plus and minus formula branches must use the same coefficients and the same square-root term. The quadratic plus root rule uses a, b, c in Positive branch root = (-b+sqrt(b × b-4 × a × c)) ÷ (2 × a); read each symbol as the field named on this page.

Interpreting another set of values

For quadratic plus root, the fields labeled a, b, c are the known quantities. The calculator solves for positive branch root using Positive branch root = (-b+sqrt(b × b-4 × a × c)) ÷ (2 × a). Interpret the answer in the context of the entered equation or coordinate system. A root, signed slope, intercept, distance, and remainder have different meanings and different valid domains. When comparing two calculations, keep their units and input definitions identical.

For a second quadratic plus root check, keep the other default inputs fixed and change b from -3 to -5. Positive branch root changes from 2 to 4.561553. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

A quadratic needs a nonzero leading coefficient. The displayed root branches describe real results only when the discriminant is nonnegative. A rounded root may not make the polynomial exactly zero after substitution; use a reasonable tolerance when checking decimal output. The reported positive branch root is 2 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.