vpa doesnt transform the roots of a polynomial equation to numerical results

syms x k

eq1 = x^3 - x*k^2 + 2*k*x^2 + 2*k^3 == 0;

sol = solve(eq1,x);

vpa(sol)

in the code above, although i use the vpa command i still get the following result:

ans =

root(z^3 + 2*k*z^2 - k^2*z + 2*k^3, z, 1)

root(z^3 + 2*k*z^2 - k^2*z + 2*k^3, z, 2)

root(z^3 + 2*k*z^2 - k^2*z + 2*k^3, z, 3)

Answer 1

[John D'Errico]

You want numerical roots, for completely general k? Brute force is a problem, since those roots would still be a function of k. so vpa still probably sees k in there and gives up.

However, if you think about what you have written, then you might try the transformation

y = x/k

Now what happens? As long as k is non-zero, then just divide that equation by k^3. Can you now write it in terms of y? Do you even need the symbolic toolbox to do that? Yes, you could use a substitution, and then call vpasolve appropriately. In terms of y, you now have:

y^3 + 2*y^2 - y + 2 = 0

xsol = vpasolve( y^3 + 2*y^2 - y + 2 == 0)*k
xsol =
                                          -2.658967081916994079346775156784*k
 k*(0.32948354095849703967338757839201 - 0.80225455755741079349558767590419i)
 k*(0.32948354095849703967338757839201 + 0.80225455755741079349558767590419i)

Just as easy is to use roots. then multiply by k to recover x, as a function of k. I suppose that leaves the numbers in a rational number form though.

x = roots([1 2 -1 2])*k
x =
                                      -(2993730789827947*k)/1125899906842624
 k*(5935447809141593/18014398509481984 + 7226066652943669i/9007199254740992)
 k*(5935447809141593/18014398509481984 - 7226066652943669i/9007199254740992)

Answer 2

[Ameer Hamza]

You need to specify the value of 'k' to get a numerical solution

syms x k
eq1 = x^3 - x*k^2 + 2*k*x^2 + 2*k^3 == 0;
sol = solve(eq1,x);
vpa(subs(sol,k,1))

Result

ans =
 0.32948354095849703967338757839201 - 0.80225455755741079349558767590419i
 0.32948354095849703967338757839201 + 0.80225455755741079349558767590419i
                                        -2.658967081916994079346775156784