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Modified and generalized equations of the fourth degree

Lecture



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 Modified and generalized equations of the fourth degree . Among all the equations of the fourth degree Modified and generalized equations of the fourth degree these equations are distinguished by the fact that for their coefficients the following relationship holds true:

Modified and generalized equations of the fourth degree

see also

return equation

algebraic equation

created: 2014-10-05
updated: 2023-06-08
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HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS

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