How to Use the Quadratic Equation Solver with Factoring & Roots
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1
Enter the quadratic coefficients a, b, and c for the standard form ax² + bx + c = 0 (where a ≠ 0).
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2
Inspect the discriminant Δ = b² - 4ac to determine root characteristics (two distinct real, one repeated, or complex conjugates).
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3
Review both root values (x₁ and x₂), including imaginary (i) representations if Δ < 0.
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4
View the parabola vertex coordinates (h, k) and axis of symmetry x = -b/(2a).
Practical Example & Use Case
Common Real-World Scenario
Solving 2x² - 4x - 6 = 0 yields discriminant Δ = 64, roots x₁ = 3, x₂ = -1, and vertex at (1, -8).
Technical Notes & Limitations
Browser Engine Architecture
Solves second-degree polynomial equations with exact algebraic and floating-point numeric precision.
Frequently Asked Questions
What happens when the discriminant is negative?
When Δ < 0, the parabola does not cross the x-axis, producing two complex conjugate roots in the form u ± vi where i = √(-1).