Explanation and example

The equation has the form ax² + bx + c = 0, where a must be nonzero. Its discriminant D = b² − 4ac determines the number of real roots. The vertex has horizontal coordinate −b/(2a). With two roots, their sum and product provide a Viète check.

Example: x² − 5x + 6 = 0 has D = 1 and roots 2 and 3. Their sum is 5 = −b/a and their product is 6 = c/a. Substitution into the original equation checks each root.

Limits

A negative discriminant means there are no real roots; this tool does not compute complex roots. The plot illustrates the function within a chosen scale while numeric answers remain available as text. Extreme coefficients may limit floating-point precision.