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

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.

• If $F(x) =x^2-1$ then $x^*$ could be either $-1$ or $1$. Jan 10, 2023 at 20:09

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.