Quartic Equation Calculator

Solve quartic (4th degree) equations and find all real and complex roots.

Enter Coefficients

ax⁴ + bx³ + cx² + dx + e = 0

Equation

1x⁴ -10x³ + 35x² -50x + 24 = 0

Roots

Complex Roots

x = 2.5 + 0.75i

x = 2.5 - 0.75i

x = 2.5 + 0.75i

x = 2.5 - 0.75i

Summary

0 real roots, 4 complex roots

About Quartic Equations

Ferrari's Method

Quartic equations are solved using Ferrari's method, which reduces the problem to solving a cubic equation (called the resolvent cubic) and then two quadratic equations.

Nature of Roots

  • • A quartic can have 0, 2, or 4 real roots
  • • Complex roots always come in conjugate pairs
  • • The sum of all roots = -b/a (Vieta's formulas)
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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

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Formula Source: Handbook of Mathematical Functions

by Abramowitz & Stegun

🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.