Question

Find the complex zeros of the polynomial function. Write f in factored form
f(x)=x^3+1
Reduce fractions and simplify roots

Answer 1

I'd try the factor (x+1) first.

Answer 2

I have no clue how to do any part of this problem

Answer 3

Synthetic Division?
Long Division?

You need to have a clue unless you have been sleeping through class.

Answer 4

I have looked at the examples given to me for the last 5 problems and I just get real confused

Answer 5

tkhunny my class in all online

Answer 6

hmmm \(x^3+1 \implies x^3+1^3\)

Answer 7

I can buy the online argument. That can be tricky.

Did you study factoring?

Answer 8

no not really. The class is only about 5wks long. it's done in 9 days

Answer 9

I don't think online classes including not covering material before exercises

Answer 10

this question is the sum of 2 cubes... and the basic structure is

\[a^3 + b^3 = (a +b)(a^2 -ab + b^2)\]

you don't need polynomial or sythetic division

just recognise a = x and b = 1 then substitute

for the quadratic you will need to use the general quadratic formula to find the complex roots

Answer 11

this is intro to college math 1

Answer 12

that is what the answer for the example looks like

Answer 13

You have to solve this equation:
x^3+1=0
or
x^3=-1
One obvious solution is x=-1, since (-1)(-1)(-1)=-1
By división bt (x+1) you can find the rest :
(x^2-x+1)
so:
x^3+1=(x+1)(x^2-x+1)
to find the other 2 complex roots just use standart method of disciminant

Answer 14

so type x^3+1=(x+1)(x^2-x+1) that into my website I use

Answer 15

no. You are asked for the roots. Find the roots of x^2-x+1=0 now

Answer 16

\(x=\huge \frac{1 \pm \sqrt{1-4}}{2}=\frac{1\pm i\sqrt{3}}{2}\)

Answer 17

what is the + with the line under it

Answer 18

plus minus

Answer 19

yea, i've seen it just didn't know what it meant

Answer 20

so now the equation thing you gave is that a step closer to the answer?

Answer 21

I gave you the answer. Complex roots are: (1/2)+i(sqrt3)/2 and (1/2)-i(sqrt3)/2

Answer 22

the thing a bit above is wrong

Answer 23

i don't think so

Answer 24

\(x^3+1=(x+1)( \frac{1}{2}+i\frac{\sqrt3}{2})( \frac{1}{2}-i\frac{\sqrt3}{2})\)

Answer 25

this is factored form that you are asked for