Solving a Quartic Equation by a general formula




At this web page you are able to solve an equation of
the fourth degree. This equation can be described by
the following general expression:

F(X) = AX4 + BX3 + CX2 + DX + E

X is an unknown real or complex number.
F(X) is a function of X. May also have the symbol 'Y'.
A, B, C, D and E are all real numbers of constants.

If you set F(X) = 0, the equation can be solved.


Example

X4 - 4X3 + 4X2 + 16X - 32 = 0

This equation has got two real and two complex roots:
X1 = -2, X2 = 2, X3 = 2 - i2 and X4 = 2 + i2.
I've drawn the graph of F(X):
F(X) = X4 - 4X3 + 4X2 + 16X - 32, [-6,7.5]:

A graph of F(X) = X4 - 4X3 + 4X2 + 16X - 32

AX4 + BX3 + CX2 + DX + E = 0


Calculation

Input the values of A, B, C, D and E.
To start the calculation please press the button.

If the calculation does not work, try to first
multiply all constants with -1.


A =    B =    C =    D =    E = 

   


X1 = 
X2 = 
X3 = 
X4 = 



Algebra