What does the $^* $ in $f(x^*) = 0$ mean?

Question

I have this question I am trying to solve:

Consider the case $F (x) = x^3 − x^2$

a.) Find the exact solutions of $F (x^∗) = 0$ by polynomial factorisation.

b.) For which of these solutions $x^∗$ is the convergence of Newton’s method quadratic(with order 2) and for which is it only linear (with order 1)? Justify your answer bystudying the properties of $F (x)$ at $x^∗$.

I was wondering what the $^*$ in $x^*$ is supposed to mean. I have tried looking online but haven't had any luck.

Cheers.

Answer 1

In this context, $x^*$ is just a composite symbol for a variable, similar to $x_0$. This particular symbol is commonly used for the solution to an equation, optimization problem, or similar such thing. By contrast something like $x_0$ is usually some sort of "starting point" that is given rather than needing to be determined. But this is just convention.