Quartic Equation Calculator
Solve fourth-degree polynomial equations (ax⁴ + bx³ + cx² + dx + e = 0) with step-by-step solutions
Equation Coefficients
Solution Results
Your Equation:
Enter coefficients to display equation
Roots of the Equation
Root 1 (x₁):
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Root 2 (x₂):
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Root 3 (x₃):
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Root 4 (x₄):
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Enter coefficients to analyze the nature of the roots.
Solution Steps
Detailed solution steps will appear here after calculation.
📈 Equation Graph
📚 About Quartic Equations
General Form
ax⁴ + bx³ + cx² + dx + e = 0
where a ≠ 0
Solution Methods
Ferrari's method, Descartes' method, factoring (when possible), or numerical approximation
Nature of Roots
Can have 4 real roots, 2 real and 2 complex roots, or 4 complex roots (as conjugate pairs)
Special Cases
Biquadratic (ax⁴ + cx² + e = 0), depressed quartic (t⁴ + pt² + qt + r = 0), or factorable forms
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Note: This calculator provides exact solutions when possible and numerical approximations for complex cases. Some quartic equations may not have simple algebraic solutions.