how can I solve a 5th order polynomial, with 1 real root. I am interested in that real root only. Numerical techniques like Newton Raphson will not work, because I want analytical solution for that real root in terms of the coefficients.
Thank you in Advance
Soumen
Hello,
The steps we use to solve fifth-degree polynomial equations are as follows: Rewrite the equation to get a polynomial, P(x), in standard form on one side of the equation and 0 on the other side. Use the rational roots theorem to find possible rational roots of P(x).
PDF is attached.
https://www.youtube.com/watch?v=SCvB7NFnl2c
Thanks,
You can solve it using »Mathematica«. And there is an option to filter the real solutions only. See the attached PDF.
If you don't have access to »Mathematica« you can also use the gratis application »wxMaxima«. e.g. with the command realroots(y^5 -3*y^4-13*y^3+y²-4*y +30); you calculate all real roots as fractions and with realroots(y^5 -3*y^4-13*y^3+y²-4*y +30),numer; as numbers [y=-2.705005*10^0,y=1.206476*10^0,y=5.374163*10^0]
Smrity Dwivedi thanks a ton for replying, i will go through the technique mentioned. But it seems that, as per Galois theory any algebraic equation with order greater than or equal to 5, is unsolvable in general. MATLAB can give roots although, but I am interested in analytical expression of the real unknown root.
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