What are zeros of a quadratic?
The solutions of ax²+bx+c = 0; where the graph crosses or touches the x-axis for real roots.
Zeros Calculator
Solve ax² + bx + c = 0 and see the discriminant and root types.
Enter quadratic coefficients
Provide a, b, and c for ax² + bx + c = 0 (a ≠ 0).
About this calculator
How to use Zeros Calculator, plus the formulas and logic behind the results.
Tool description
Zeros (roots) are x-values where the quadratic equals zero. The discriminant b²−4ac classifies the solutions.
How to use
- Enter coefficients a, b, and c.
- Ensure a is not zero.
- Select Calculate.
- Read the roots and discriminant.
Formulas & reference
Δ = b² − 4acx = (−b ± √Δ) / (2a)
Discriminant guide
- Δ > 0: two distinct real roots
- Δ = 0: one repeated real root
- Δ < 0: complex conjugate roots
- Example: x²−5x+6 → 2 and 3
Calculation logic
Uses the quadratic formula. Negative discriminants produce a complex conjugate pair displayed in a±bi form.
If a = 0 the equation is not quadratic.
Zeros Calculator FAQ
Common questions about this calculator and how to use the results.
What is the discriminant?
Δ = b²−4ac; it tells how many real roots exist.
Can roots be complex?
Yes when Δ < 0; this tool reports them as a±bi.
Why must a ≠ 0?
Otherwise the expression is linear, not quadratic.
Are double roots listed twice?
They are reported as a repeated root (multiplicity 2).
Does factoring always work?
Not easily over the reals when Δ < 0; the quadratic formula always works.