For the polynomial f(x)=x^3-x^2-4x-4
How many zeros does the function have over the set of complex numbers?

Question

For the polynomial f(x)=x^3-x^2-4x-4
How many zeros does the function have over the set of complex numbers?

aum · Answer

Apply Descarte's Rule of Signs.

samsan9 · Answer

is that the one with the sign changes?

aum · Answer

yes.

anonymous · Answer

@aum I feel like I did something wrong can you please check

aum · Answer

$f(x) = (x^{3}-x^{2})-(4x+4)$         (4x+4) instead of (4x-4)

samsan9 · Answer

what does find the zeroes mean? does that mean to plug in the zeros into the variables?

aum · Answer

zeros are the x values that will make the function zero.
If you graph the function, it will cross the x axis at those zeros.

anonymous · Answer

sam can you check your equation again? : o make sure the signs are correct?

samsan9 · Answer

ok hold up

samsan9 · Answer

sorry it was supposed to be a +4

anonymous · Answer

oh then I was right! xD

anonymous · Answer

$$f(x)= (x^{3} - x^{2}) -(4x-4)$$
$$f(x) = x^{2}(x-1) -4(x-1)$$
$$f(x)= (x^{2}-4)(x-1)$$
then find zeros

aum · Answer

If f(x) can be factored, no need for Descarte's Rule of Signs.
Factor, equate it to zero and solve for x.

samsan9 · Answer

so x^2-4=0 and x-1=0?

anonymous · Answer

Yes :)

anonymous · Answer

Thank you @aun, you're super smart!
I'll look up that rule :)

samsan9 · Answer

i got x=2 and x=1

aum · Answer

Thanks study100. You are smart for catching the sign error in the original posting.

anonymous · Answer

x^2 = 4
x= plus minus 2

samsan9 · Answer

yeah this is the second time lol sorry about that and and oh yeah once its square rooted that means its like  plus or minus everything right?

anonymous · Answer

Yes :) so 3 zeros

samsan9 · Answer

yes thanks to both of you