Quartic Equation Solver

Solve quartic equations ax⁴+bx³+cx²+dx+e=0. Free online quartic equation calculator.

The Quartic Equation Solver finds all roots of fourth-degree polynomial equations. Using Ferrari's method and numerical techniques, this calculator handles all cases including multiple real roots and complex conjugate pairs. Enter your coefficients to find all four solutions to any quartic equation.

Common use cases

  • Advanced physics problems
  • Engineering calculations
  • Optics and lens design
  • Mathematical research
  • Competitive mathematics

How to use

  1. Enter coefficients a through e
  2. a for x⁴, b for x³, c for x², d for x, e for constant
  3. Click solve for all roots
  4. View real and complex solutions
  5. See the solution process

FAQ

How many roots does a quartic have?

Exactly 4 roots (counting multiplicity and complex). Could be 4, 2, or 0 real roots with complex conjugate pairs.

Is there a quartic formula?

Yes, Ferrari's formula (1545) solves quartics algebraically, though it's very complex.

Can I solve x⁴ = 16?

Yes, enter a=1, b=c=d=0, e=-16. Solutions: x=2, x=-2, x=2i, x=-2i.

What about quintic and higher?

Degree 5+ have no general algebraic solution (Abel-Ruffini theorem). Use numerical methods.