- Root 1
- 3
- Root 2
- 2
- Discriminant
- 1
How it works
Move every term before copying coefficients
For x² = 5x − 6, rewrite the equation as x² − 5x + 6 = 0, then enter 1, −5 and 6. Copying the right-hand signs directly would solve a different equation.
Reading the roots of a quadratic equation
Write the equation in the standard quadratic form before entering its coefficients, including any negative signs and a zero coefficient for a missing linear term. The roots are the input values where the expression equals zero. The discriminant helps explain whether the roots are distinct, repeated, or non-real under the supported output. A zero leading coefficient describes a different type of equation.
Quadratic roots: formula and assumptions
x = (−b ± √(b² − 4ac)) / (2a).
The discriminant identifies two real roots, a repeated root, or two complex roots. If a is zero, the equation is linear.
Worked example
Using the Quadratic roots example:
- a
- 1
- b
- -5
- c
- 6
x = (−b ± √(b² − 4ac)) / (2a).
Example result
Root 1: 3
Root 2: 2
Discriminant: 1
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
What does the discriminant tell me?
A positive discriminant gives two real roots, zero gives a repeated real root, and a negative value gives complex roots.
What happens if the coefficient of x squared is zero?
The equation is no longer quadratic. The calculator treats the remaining expression as a linear or degenerate equation.
Prepared by Finflo. See our methodology and editorial policy.