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Quadratic Formula Calculator

Solve ax² + bx + c = 0: get the discriminant, both roots and the nature of the solutions.

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Enter a, b, c and the Quadratic Formula Calculator works out Discriminant (b² − 4ac), Root 1, Root 2, Nature of roots straight away. For instance, with a = 1, b = -3 and c = 2 it returns Discriminant (b² − 4ac) = 1, Root 1 = 2 and Root 2 = 1.

How to use it

  1. Enter your values: a, b, c.
  2. Read the result instantly: Discriminant (b² − 4ac), Root 1, Root 2, Nature of roots.

Frequently asked questions

How does the Quadratic Formula Calculator work?

It takes a, b and c and derives Discriminant (b² − 4ac), Root 1, Root 2 and Nature of roots from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

3 values: a, b and c. Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With a = 1, b = -3 and c = 2, the calculator returns Discriminant (b² − 4ac) = 1, Root 1 = 2 and Root 2 = 1. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

What is the difference between the Quadratic Formula Calculator and the Primitive root calculator?

This one returns Discriminant (b² − 4ac) and Root 1; the Primitive root calculator returns Primitive roots exist? and Smallest primitive root. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Distance Formula Calculator is the closest one after this: Find the distance between two points on an interactive coordinate plane, with the Pythagorean working, the midpoint, the slope and the direction angle.

What else is worth having open alongside it?

Triangle area calculator (Heron's formula) and Cube root calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from, and how current are they?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.
Quadratic Formula Calculator — OneKitly