Fundamental theorem of algebra says: Polynomial of degree n

Actually its n complex roots counted with multiplicity. In that case there is only one unique root, which is 0, but the fundamental theorem of algebra only states that the unique roots are at most n.

>>8561648
LOL so you can say...function has 2000 roots

But there all the same...

LOL

just like I have 2000 life's

but they're all the same life at the same time LOL

>>8561660
>shit posting on Christmas
What a sad man you are.

>the polynomial doesn't exist! got you!

>>8561660
derive your polynomial function, you still get one root from the primitive, which is zero
then, try deriving your fucking life faggot

>>8561640
>Polynomial of degree n has *at most* n roots.
FTFY

>>8561960
not OP but he's right about one thing, they teach you at most n roots cause a lot of highschoolers taking algebra are fucking retarded and wouldn't understand what complex roots are but it's actually just exactly n roots.

>>8561960
>>Polynomial of degree n has *at most* n roots.

This statement is actually weaker than the fundamental theorem of algebra which states that a polynomial of degree n has EXACTLY n roots, counting multiplicity.

So in the case of x^2, 0 is a second degree roots. It is a double root. It counts as two roots.

>>8561640
fuck off brindle

>>8562026
>>8562042
[math]\displaystyle x^4+4x^3+6x^2+4x+1=0[/math]
has one root, fgt pls

>>8563303
has one unique root of -1, with mutiplicity of 4, not coincidentally the degree of the polynomial. because you can factor it to (x+1)^4 = 0, and each factor has -1 as a root

>>8561640
what is multiplicity

>>8561640
That's literally a "double root", a root of a polynomial is simply when f(x) = 0.

[math] f(x) = x^2 = 0 [/math] does have two roots, like you pointed out, +/-0. The polynomial crosses down and comes back up at -0, and +0 respectively. Simply because both roots are on the same point on a number line doesn't imply it "only has one root", any root of any term with an even n can do this, cross n/2 and come back up n/2 times at the same point. Hence why
>>8563303
has 4 roots, it crosses down, comes back up, crosses back down, and comes back up one last time

Similarly odd n terms can cross, any multiple of times as long as the curve does not cross the axis again until another terms root.
Ex
[math] (x+2)^3 (x+1) [/math]
has a degree three root at (-2,0) , and a degree one root at (-1,0)
n=4, and # of roots = 4, but it only graphically crosses the x axis twice.
>What is multiplicity for 400
Also it's worth pointing out
>What are complex roots for 500