I didn't understand the below from sets and functions algebra caltech pdf. The highlight is my problem. What does it mean and why does say X=0?

Question

I am not English speaking and also highlight is yellow in solution…

The graph in the fogure shows an even function $f(x) = \dfrac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are rational quadratic polynomials. Give possible formulas for $p(x)$ and $q(x)$.

Answer 1

From the first picture we are meant to see that $f(0)=0$, and also that the $x$-axis is a tangent, so that $f'(0)=0$. That's what a "second-order zero" means. That means the same is true for $p(x)$, so that $x^2$ must divide $p(x)$.

The constant $\chi$ can't be $0$ or else an $x$ on the denominator would cancel out one of the $x$s on top, and leave us with just a simple zero, not a second-order one.