Quintic Equation Calculator

x5 + x4 + x3 + x2 + x + = 0

Round to
6 decimal places 12 decimal places
x1:                                                   
x2: + i
x3: + i
x4: + i
x5: + i


Instructions:
This calculator solves equations of the form Ax5 + Bx4 + Cx3 + Dx2 + Ex + F = 0, so if your equation is not in this form already, perform the necessary algebra to do so.
Plug in the coefficients into each box. If the equation has a 'missing term' (for example, no X2 term), then enter it as a zero. Do not leave the field blank

Due 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 Ax5 + Bx4 + Cx3 + Dx2 + 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.