|Dec3-12, 05:47 AM||#1|
talor series expansion of roots of algebraic equation
I have a algebraic equation like so:
the roots are obviously-
How can I expand the expression for the roots- as a taylor series?
the answer is given as:
I am assuming the author expanded the root 'x' in terms of ε before hand and substituted in the algebraic.Is that even allowed?
|Dec3-12, 03:17 PM||#2|
Use the binomial theorem on √(1+ε^2/4) = (1 + ε2/4)1/2 = 1+ε2/8 + O(ε4)
|Similar Threads for: talor series expansion of roots of algebraic equation|
|Roots lying between the roots of a given equation||Precalculus Mathematics Homework||9|
|Algebraic Expansion with complex numbers||Precalculus Mathematics Homework||8|
|Solution of two first order differential equation with one algebraic equation.||Differential Equations||2|
|Partial Fraction Expansion with repeated & complex roots||Differential Equations||4|
|Partial Fraction Expansion with repeated roots||Differential Equations||6|