Is the following statement is true ?
There exist polynomials $f(x)$ and $g(x)$, with complex coefficients, such that$ \left(\frac{f(x)} {g(x)}\right)^ 2$ =$ x$.
i thinks it is true because $\frac{f(x)} {g(x)}$ =$x^{1/2}$ which contain both + and - that is every complex number is real number so this satetment is true
It is false. If it was true, you would have $(f(x))^2=x(g(x))^2$. But the first polynomial has even degree, whereas the second one has odd degree.