Quintic Equation Calculator |
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x_{1}: |

x_{2}: + i |

x_{3}: + i |

x_{4}: + i |

x_{5}: + i |

Instructions:This calculator solves equations of the form Ax, so if your equation is not in this form already, perform the necessary algebra to do so.^{5} + Bx^{4} + Cx^{3} + Dx^{2} + Ex + F = 0Plug in the coefficients into each box. If the equation has a 'missing term' (for example, no X ^{2} term), then enter it as a zero. Do not leave the field blankDue to round-off errors, some answers may be slightly off. |

This calculator computes real and complex roots for any quintic polynomial in the form of **Ax ^{5} + Bx^{4} + Cx^{3} + Dx^{2} + EX + F = 0** where A, B, C, D, E, and F are real numbers and A is non-zero. It applies the

**Newton-Raphson Method**to iteratively find a root to the Quintic, starting out with a random initial guess. Then it factors the equation out to a linear and a quartic equation and then solves the left-over quartic equation for roots 2 through 5.

**The Newton-Raphson Method can occasionally run into division by zero issues**. When this happens, the error message '

**cannot solve, attempted division by 0**' will occur. Since the initial guess is randomized each time the 'Calculate' button is pressed, another trial may result in a solution.