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)