Quartic Equation Calculator

How to solve a quartic equation using Quartic Equation Calculator

Quartic Equation Calculator solves quartic, cubic, quadratic and linear equations, including equations with fractions and parentheses. Just type in any equation you want to solve and Quartic Equation Calculator will show you the result.

Quartic Equation Calculator supports the predefined format (in the Settings window) for quartic equations (or fourth degree equations) in the general form:
ax⁴ + bx³ + cx² + dx + e = 0.
To solve a fourth degree equation, enter the coefficients 'a', 'b', 'c', 'd' and 'e' and press 'Solve'. The coefficients 'a', 'b', 'c', 'd' and 'e' are real numbers, a ≠ 0. Note: for a missing term enter zero.

Quartic Equation Calculator displays the original equation and the result.

Quartic Equation Calculator supports positive, negative, or zero values of the coefficients.

Solving a fourth degree equation (quartic equation)

(1)

1. Using the substitution we get the depressed equation (2),   where



2. If , we will solve

If , then this equation always has a positive root

The roots of the original quartic equation (1) can be obtained by the formulas



3. If q = 0, then the reduced equation (2) becomes a biquadratic equation

And the four roots of this equation can be found by the formulas



4. You can estimate the solutions with the corresponding discrepancies



The less is, the more accurate the solutions are. For a more accurate estimate is reasonable to consider the relative error.

Solve the equation and calculate the corresponding discrepancies

Then the relative discrepancies can be calculated