Find the roots of a complicated expression

Is it possible find the roots of a complicated expression like this:

-190 + 100/(1+0.01+x) + 80/(1+0.02+x)^2 + 20/(1+0.03+x)^3

Is there a way to rearrange this into a polynomial first, and then seek its roots?

(It would be easy if the denominators in the expression were simply (1+x), but in this complicated expression each denominator is different.)

Answer 1

[Walter Roberson]

format long g
syms x
y =  -190 + 100/(1+0.01+x) + 80/(1+0.02+x)^2 + 20/(1+0.03+x)^3

y = 

xsol = solve(y)

xsol = 

double(xsol)

ans = 
         0.0141995305746602 +                     0i
          -1.01003015681544 +                     0i
          -1.02053169387449 -   0.00181744153124217i
          -1.02053169387449 +   0.00181744153124217i
          -1.28839509826828 -     0.204565386093891i
          -1.28839509826828 +     0.204565386093891i

[Tim Berry]

Thank you Walter, this is brilliant. In case it is of interest, the background to my question is I am investigating whether complex numbers can occur in various problems. Cheers!

Answer 2

[Torsten]

syms x
expr_orig = -190 + 100/(1+0.01+x) + 80/(1+0.02+x)^2 + 20/(1+0.03+x)^3;
expr = expr_orig*(1+0.01+x)*(1+0.02+x)^2*(1+0.03+x)^3;
expr = simplify(expr)
c = sym2poly(expr);
sol = vpa(roots(c));
format long
sol

[Tim Berry]

Thank you so much Torsten, this is fantastic. In case it is of interest, the background to my question is I am investigating whether complex numbers can occur in various problems. Cheers!