Quartic Equation Calculator

Quartic Equation Calculator

Quartic Equation Calculator solves a wide range of quartic, cubic, quadratic and linear equations, including equations with fractions and parentheses.
With the Advanced format, you can input equations in any form.

Unit Converter and 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)

quartic equation (1)

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

solve quartic equation solve quartic equation

2. If q is not zero , we will solve cubic equation

If q is not zero, then this equation always has a positive root z0

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

roots of the quartic equation

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

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

roots of biquadratic equation

4. You can estimate the solutions with the corresponding discrepancies

solutions with the corresponding discrepancies

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

Solve the equation quartic equation and calculate the corresponding discrepancies Discrepancy

Then the relative discrepancies Discrepancy can be calculated Discrepancy

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Wednesday, September 18, 2019

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