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 . 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
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HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS
Terms: HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS