What is the discriminant?
The discriminant (b² - 4ac) determines the nature of the roots. If positive, 2 real roots. If zero, 1 real root. If negative, 2 complex roots.
Calculator
Enter your values
Results
Roots
x₁ = 2.000
x₂ = 1.000
Two Real Roots
Discriminant
1.00
Vertex
(1.50, -0.25)
Analysis
Interpretation of the current calculator output
Calculation Summary
The current inputs have been processed for the quadratic formula calculator. Review the results panel for the computed output and use the charts tab to compare the current values visually.
How to Read It
The main result shows the direct answer for your current inputs. Supporting sections below explain the method, example, and common questions so the result is easier to interpret.
How to Use
Step-by-step instructions
- 1Enter the coefficients a, b, and c.
- 2The calculator computes the roots and discriminant.
- 3View the graph of the parabola.
Quadratic Formula
Finds the roots (x-intercepts) of a quadratic equation using the coefficients a, b, and c.
x = (-b ± √(b² - 4ac)) / 2aVariables:
aCoefficient of x²bCoefficient of xcConstant termExample
x² - 3x + 2 = 0
Inputs:
a:1
b:-3
c:2
Steps:
- 1.D = (-3)² - 4(1)(2) = 1
- 2.x = (3 ± 1) / 2
- 3.x1 = 2, x2 = 1
Result:
x = 2, 1