The quadratic formula solves equations in standard form, while the expression inside the square root provides information before either root is calculated. That expression is the discriminant, and its sign identifies the type of solutions.
By Calqoras Editorial Team • Reviewed September 1, 2026
The quadratic formula solves equations in standard form, while the expression inside the square root provides information before either root is calculated. That expression is the discriminant, and its sign identifies the type of solutions.
Write standard form first
Move every term to one side so the other side equals zero, then identify a, b and c in ax squared plus bx plus c. Include signs carefully and enter zero for a missing term.
Confirm the leading coefficient
The coefficient a cannot be zero. Without the squared term the equation is linear, and applying the quadratic formula would require division by zero.
Interpret the discriminant
A positive discriminant produces two distinct real roots. Zero produces one repeated real root. A negative value produces a complex conjugate pair and no real horizontal-axis intersections.
Substitute to check
Place each calculated root back into the original equation. Small non-zero differences may come from rounding, but a large remainder usually indicates a sign, input or arithmetic error.
Quick reference table
| Item | Meaning or example |
|---|---|
| Discriminant > 0 | Two real roots |
| Discriminant = 0 | One repeated root |
| Discriminant < 0 | Two complex roots |
| a = 0 | Not a quadratic equation |
Reference and further reading
This guide is general educational information. Continue with Wolfram MathWorld — Quadratic Formula and verify important figures independently.
This article is general educational information prepared by the Calqoras Editorial Team. Verify important figures independently and consult a qualified professional where appropriate.
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