Question

How does the Fundamental Theorem of Algebra tell you how many roots there are?

My teacher asked this when I did this for my homework:
The Fundamental Theorem of Algebra can be used to find the maximum number of all zeros for a function. To find the number of complex zeros, just subtract the number of real zeros from the total number of zeros.

So basically I wrote what they do, but not how they work.

Answer 1

that looks good to me ! also add what fundamental theorem of algebra tells you exactly

Answer 2

Well it isn't good., because that is what I wrote and my teacher said I didn't say "why" it works!

Answer 3

I think she is looking for the statemetn of theorem

Answer 4

Fundamental theorem of algebra says that a polynomial of degree `n` has exactly `n` zeroes

(conditions apply)

Answer 5

add that line to the start of your answer

Answer 6

Ohhh I see what you mean. Haha that's so simple I can't believe I didn't see that that is what she was asking for haha, thanks!!!

Answer 7

np :) keepin mind that "exactly `n` zeroes " requires you to count the multiplicity of a zero also.

Answer 8

example :
f(x) = x^2 - 2x + 1

heredegree = `2`,
so by fundamental theorem of algebra this polynomial has exactly `2` zeroes : 1, 1

Answer 9

it may look bit weird counting a single number 1 as two zeroes
but notice that the theorem never said `n distinct zeroes`

Answer 10

ohh gotcha!!! Thanks!