Foundations, part 5

$\large P(z) = \sum_{n=0}^{5} a_nz^n \sum_{n=0}^{9} b_nz^n$

where $a_n, b_n \in \mathbb{R}$ for all $n$ , $a_5\neq 0$ , $b_9\neq 0$ .

Then counting roots with multiplicity we can conclude that $P(z)$ has $\text{\_\_\_\_\_\_\_\_\_\_\_} .$

For more , Try this set