Quadratic Equation: Your Questions Answered
These are the questions people ask most often about quadratic equation. Each answer is short; follow the links for the full detail.
What does a quadratic equation calculation tell me?
Solves ax² + bx + c = 0.
What is the formula?
x = (−b ± √(b² − 4ac)) ÷ 2a.
What do I need to enter?
a, b, c.
Can I use any units?
Yes, as long as every input uses the same unit. The answer will be in that unit (squared for areas, cubed for volumes).
Can you show an example?
For example, with these inputs:
- a: 1
- b: -5
- c: 6
the calculator returns:
- Roots: x₁ = 3, x₂ = 2
- Discriminant: 1
Any tips?
- Estimate the answer roughly first so you can spot a result that is clearly wrong.
- Write down the formula before plugging numbers in; it prevents mixing up variables.
- Check your answer by working backwards from the result.
Background
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
Related calculations
- Perimeter of a Triangle Calculator: Calculates the perimeter of a triangle from the measurements you enter.
- Perimeter of an Ellipse Calculator: Calculates the perimeter of an ellipse from the measurements you enter.
- Arc Length Calculator: Calculates the arc length from the measurements you enter.
- Volume of a Cube Calculator: Calculates the volume of a cube from the measurements you enter.
Try it yourself with the Quadratic Equation Solver.
Run your own numbers: Quadratic Equation Solver