the degree of the polynomial will determine the number of zeros in it..
take these examples
a.)x - 4 = 0
x = 4 -----one zero
b.) x²+2x+1=0 ------>(x+1)(x+1) = 0
x = -1, x= -1 ---two zeros
c.) x³ - 4x = 0
x(x² - 4) = 0
x(x-2)(x+2)=0
x = 0, x = 2, x = -2 ----three zeros
therefore knowing that the polynomial is in 9th degree, we can conclude that there are at most 9 zeros..
