How many complex roots does a polynomial of degree 9 have? I know the answer is 9 but why?

Question

campbell_st · Answer

well a degree 9 polynomial will have 9 roots or zeros.... as to whether they are real of complex or a combination is dependent upon the equation

anonymous · Answer

is whatever the degree the polynomial has = the number of roots/zeros

whpalmer4 · Answer

for a polynomial in a single variable, yes.

ranga · Answer

And real numbers are a subset of complex numbers where in a + bi, b = 0.

campbell_st · Answer

thats correct.... the degree always matches the number of zeros... 

but in some cases they can be repeated zeros... 

y = (x +3)^2 

is a quadratic with 2 zeros.... but they are repeated... x = -3 and x = -3... 

that's the trick.... perfect squares have 2... just they are repeated

ranga · Answer

So a 9th degree polynomial will have a maximum of 9 distinct complex roots.

anonymous · Answer

thanks guys!

ranga · Answer

you are welcome.