Question
What does the discriminant tell you?
The discriminant shows how many real roots a quadratic has and whether those roots are distinct, repeated, or not real.
Math
Use OmniCalc's quadratic formula calculator to solve ax² + bx + c = 0 and inspect the discriminant and roots quickly.
Quadratic formula calculator
Enter coefficients a, b, and c to find the discriminant, real roots, axis of symmetry, and vertex behavior in one place.
Why this result matters
A focused algebra follow-on from scientific calculator, log, and exponent pages for equation-solving intent. Use the tool above to enter a few clear inputs and get a practical answer you can use right away.
This quadratic formula calculator helps students solve quadratic equations fast while also showing the discriminant, roots, axis of symmetry, and related parabola details. It is useful for algebra homework, exams, and quick checking.
Formula and method
The quadratic formula uses x = (-b ± √(b² - 4ac)) / 2a, where the discriminant decides whether the equation has two real roots, one repeated real root, or no real roots.
Example
If you enter a = 1, b = -3, and c = 2, the calculator returns roots 2 and 1.
FAQ
Short answers to the questions people often ask before or after using the tool.
Question
The discriminant shows how many real roots a quadratic has and whether those roots are distinct, repeated, or not real.
Question
A negative discriminant means the quadratic has no real roots, though it still has complex roots.
Question
If a equals zero, the equation is no longer quadratic, so the quadratic formula does not apply.
Related calculators
If the next question is close to this one, these are the best pages to open next.
Math
Use OmniCalc's Pythagorean theorem calculator to solve right-triangle side lengths by finding a hypotenuse or a missing leg instantly.
Math
Use OmniCalc's slope calculator to find the slope between two points instantly, along with rise, run, midpoint, and distance.
Math
Use OmniCalc's root calculator to find square roots, cube roots, and higher-order roots instantly.
Math
Use OmniCalc's scientific calculator for powers, roots, logs, trig, and core arithmetic in one place.