Why do only real roots intersect x axis for an equation?

Question

If we draw graph of an equation with y = f(x) we see that x axis is intersected for only real roots of the equation. Y value can be zero for complex roots as well. Why then is this so? What is an intuitive explanation of this?

Answer 1

What you call “graph” is the set of all pairs $\bigl(x,f(x)\bigr)$ where $x$ belongs to the domain $D_f$ of $f$, or, to more precise, to the real numbers within $D_f$. It is a subset of $\mathbb{R}^2$. Therefore, it cannot possibly show you the non-real roots of $f$.

Answer 2

The x axis is a real number line