How to extract polynomial "p" from symbolic solution "root(p,x,k)"?

When using solve() symbolically and a solution of the form root(f(z),z,k) is produced, is it possible to extract f(z) without manually copying and pasting?

For instance, if I assign an example solution to variable x :

x = root(z^2 + z + 1, z, 1)

Can z^2 + z + 1 or its coefficients be extracted from x?

sym2poly() does not seem to recognize root(). I suppose I could bluntly use regexp(), though it seems there must be a simpler solution.

Related: How to remove "root(f(z), z, n)" from solve solution? - (mathworks.com)

Answer 1

[Walter Roberson]

use children() — or findSymType() and then children()

[FingersCrossed]

Perfect, thank you. Here's my use case for anyone else:

root_children = children(x);
poly = root_children{1};

[Walter Roberson]

children(x, 1)

would be shorter for that use case

Answer 2

[FingersCrossed]

Use Walter's answer instead of this. Just for fun, here is a convoluted regexp() approach:

[cell_poly,~] = regexp(string(x),'root\((.*?),','tokens','match');
poly = str2sym(string(cell_poly));