Question

1. Provide two polynomials and predict the number of complex roots for each.
2. You must explain how you found the number of complex roots for each.

Answer 1

Please Help!!

Answer 2

x^3=1
complex roots are omega & omega^2

Answer 3

now how to find................

Answer 4

huh?

Answer 5

for any quadratic equation ax^2+bx+c=0
roots are x=\[[-b \pm \sqrt{b ^{2}-4ac}]/2a\]

Answer 6

'Fundamental Theorem of Algebra'

Answer 7

this b^2-4ac is called discriminent denoted by D if it is -ve then the roots are complex for eg
x^2+x+1=0
you will get D=1-4=-3 so x=\[[-1\pm \sqrt{-3}]/2\]
now \[\sqrt{-x}=i \sqrt{x}\] where i=square root of -1
so x=-1/2+i[3^(1/2)]/2 and other one both are complex:)
do you want more on this

Answer 8

That's all very interesting, @Aperogalics , but it does not answer the question asked by @katherinekc .

Answer 9

oh sry i read it more concentratingly now:)

Answer 10

yeah i have to put these two questions into an essay form

Answer 11

paragraph*

Answer 12

i have answer for that also:)

Answer 13

@katherinekc type these phrases into a Google search:
"Fundamental Theorem of Algebra"
"Descartes' Rule of Signs"

Answer 14

but what would two polynomials be? how would i predict the number of complex roots for each.

Answer 15

You can make up the polynomials yourself. Whatever you want.

Answer 16

and then the two phrases u gave would be how i found them?

Answer 17

Research those phrases to get more background information.
For example, I typed "Fundamental theorem of algebra" into Google and got:
http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html
Check it out.

Answer 18

ok, thankyou

Answer 19

simple way is to see the sign change in any polynomial as the no. of changes there are no. of zeros and if the degree of polynomial is greater by let n then there will be n complex roots:)

Answer 20

@Aperogalics , you are not making any sense. Can you translate that into English, please?

Answer 21

let me explain by an example
:)........k