Question

Having to do with polynomial basics, what are double zeros and complex zeros?

Answer 1

A polynomial has same number of solutions as its degree.

Let me know if you need more elaboration of above statement

Answer 2

You mean... like if it was x^3 it would have 3 solutions?

Answer 3

So if you solve the polynomial of degree 3 but you only found 1 real soloution,that means the other two soloution are complex

Answer 4

Could you give me an example of a complex solution?

Answer 5

Hold on, it is coming

Answer 6

x^3+x^2+x+1
Since this is degree 3, this must have 3 soloution right

Answer 7

Right

Answer 8

So lets try to solve; find its solution

Answer 9

okay one second

Answer 10

so by factoring this
x^3+x^2+x+1
can be turned into this
(x+1)(x+1)^2

I hope you can already see what one solution is going to be

Answer 11

Right
x=-1......right..?

Answer 12

2

Answer 13

Right, so we have one solution and since (x^2+1) can't be factored there is no other real solution. But x^3+x^2+x+1 being a degree 3 poly, it must be 3 total soloution. So how many complex(or imaginary) souloutions are there?

Answer 14

So thats a complex zero, whats a double zero? Isn't that when it's like (x+3)(x+3) so its the same answer twice?

Answer 15

Yes

Answer 16

Do you know what happens at double zero? How would the graph be different from single zero?

Answer 17

The graph touches the point but doesn't cross it, right?

Answer 18

I could be way off

Answer 19

You are exactly right.

Answer 20

Alright, thank you soooo much! :)