Or, if you question is more "sage" than "math" question...

...using sympy from the SAGE-wiki help and website 
http://byumcl.bitbucket.org/bootcamp2013/labs/sympy.html :

example with no "x" symbolic and another one with symbolic "x" 

import sympy as sym
from sympy import Symbol
x = sympy.Symbol("x")
y = sympy.Symbol("y")
roots = sym.solve(y**3 + 2*y**2 + 8, y)
print(roots)
roots = sym.solve(x^2*y**3 + (5*x+3)*2*y**2 + 8*x, y)
print(roots)

and filtering the complex (with I) symbolic roots you get the real one.


On Friday, 9 January 2015 11:35:01 UTC+1, Santanu wrote:
>
> Dear all,
>
> I have one polynomial 
> f_x(y) =y^3 +f_1(x) y^2 +f_2(x) y + f_3(x). 
>
> Since it is a cubic polynomial, it has atleast 
> one real root.
> I want to find that real root  as a function of x.  
> I know that x \in [a,b]. 
>
>

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