Answer
The graph touches the x-axis at the zero, p and turns around, if p is a zero of even multiplicity. The graph crosses the x-axis at p, if p is a zero of odd multiplicity.
Work Step by Step
We know that the graph touches the x-axis at the zero, p and turns around, if p is a zero of even multiplicity. The graph crosses the x-axis at p, if p is a zero of odd multiplicity.
For example, let us consider a polynomial function $f\left( x \right)$ given by
$f\left( x \right)={{x}^{4}}-2{{x}^{2}}+1$
Put $f\left( x \right)=0$
$\begin{align}
& {{x}^{4}}-2{{x}^{2}}+1=0 \\
& ={{\left( x+1 \right)}^{2}}{{\left( x-1 \right)}^{2}}
\end{align}$
Thus, the polynomial function has $-1$ and $1$ zeros with multiplicity $2$. Thus, the graph touches the x-axis at $-1$ and $1$.
