What does the discriminant tell me before I solve?
It tells the root type: positive means two real roots, zero means one repeated real root, and negative means a complex conjugate pair.
Quadratic Formula Calculator
Solve equations in standard form ax^2 + bx + c = 0 by checking the discriminant first, then reading the real, repeated, complex, or linear result.
Start with standard form
Write the equation as ax^2 + bx + c = 0 before entering coefficients. The signs belong to a, b, and c, and the discriminant tells you what kind of roots to expect.
Solve a quadratic
- Identify a, b, and c.
- Check whether a = 0.
- Compute the discriminant.
- Solve the roots.
- Compare the roots with the vertex.
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Discriminant, roots, and vertex
Roots show x-intercepts; the vertex shows the turning point of the parabola.
Discriminant
Quadratic formula
Expanded formula
Vertex x-coordinate
Linear fallback
Discriminant cases
- D > 0 means two real roots.
- D = 0 means one repeated real root.
- D < 0 means a complex conjugate pair.
- If a = 0, the equation is linear instead of quadratic.
The vertex is extra context: roots show where the parabola crosses the x-axis, while the vertex shows where it turns. A repeated root happens at the vertex.
FAQ
What happens if a is 0?
The equation is no longer quadratic because the x^2 term disappears. If b is not 0, solve the remaining linear equation with x = -c / b.
