Re: Solution of Cubic Equations


Anton wrote:
I am trying to solve:
x^4-4x^3+8x+3=0
first i put x+y+4
and ended up with y^4-96Y^2-504Y-733
This seems weird to me.
How should I proceed?
I am followin KA Stroud 'Further Engineering Mathematics' Prog 2
Section 82.4
Any help appreciated.
I am an engineering trying to revise my degree maths after 31 years ..
not a pure mathematician!

You can use Sturm sequences for polynomials to find real roots.

E:\c\sturm>sturm
Please enter order of polynomial: 4

Please enter coefficient number 4: 1
Please enter coefficient number 3: -4
Please enter coefficient number 2: 0
Please enter coefficient number 1: 8
Please enter coefficient number 0: 3

Sturm sequence for:
1.000000 -4.000000 0.000000 8.000000 3.000000

1.000000 -4.000000 0.000000 8.000000 3.000000
1.000000 -3.000000 0.000000 2.000000
1.000000 -2.000000 -1.666667
1.000000 -1.000000
2.666667


4 distinct real roots for x: -1.000000 -0.414214 2.414214 3.000000

Code found here:
http://www.acm.org/tog/GraphicsGems/gems/Sturm/

.

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