How to Use the Quadratic & Cubic Equation Solver
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1
Select equation degree (Quadratic or Cubic).
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2
Enter the coefficients a, b, c (and d for cubic).
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3
View the roots (real and complex if applicable), discriminant, and vertex (for quadratic).
Practical Example & Use Case
Common Real-World Scenario
Solving 2x² + 5x - 3 = 0 to find roots x = 0.5 and x = -3, with discriminant = 49.
Technical Notes & Limitations
Browser Engine Architecture
Provides exact rational and irrational roots. Complex roots are displayed in a+bi form.
Frequently Asked Questions
What does a negative discriminant mean?
A negative discriminant in a quadratic means no real roots exist — the parabola never crosses the x-axis. The two roots are complex conjugates.
Can this solve ax³+bx²+cx+d=0?
Yes. Cubic equations are solved using Cardano's method. All three roots (which may include complex pairs) are displayed.