Modified and generalized equations of the fourth degree

ax ⁴ + bx ³ + cx ² - bx + a = 0. - Modified return equation.

To solve this equation, it is necessary to make a replacement:
y = x - 1 / x,
as a result, we get a quadratic equation:
ay ² + by + c + 2a = 0.

A fourth-degree generalized return equation reduces to a quadratic equation by substitution . Among all the equations of the fourth degree these equations are distinguished by the fact that for their coefficients the following relationship holds true:

see also

return equation

algebraic equation