Free Quartic Equations Calculator - Solves quartic equations in the form ax^{4} + bx^{3} + cx^{2} + dx + e using the following methods:

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

This calculator has 6 inputs.

1) Solve the long way for all roots and the discriminant Δ

2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

This calculator has 6 inputs.

f = c - (3/8b^{2})

g = d + ⅜b^{3} - ½bc

h = e - (3b^{4}/256) + (b^{2} * c)/16 - bd/4

x^{3} + ½fx^{2} + ((f^{2} - 4h)/16)x - g^{2}/64 = 0

Δ = 4b^{3} d - b^{2} c^{2} + 4ac^{3} - 18abcd + 27a^{2}d^{2}

For more math formulas, check out our Formula Dossier

g = d + ⅜b

h = e - (3b

x

Δ = 4b

For more math formulas, check out our Formula Dossier

- discriminant
- Shows how many roots and their properties a polynomial has

Δ - equation
- a statement declaring two mathematical expressions are equal
- quartic equations
- 4th degree polynomial equations
- root
- Value where a function equals zero