help finding other zeros of x^6-7x^4+16x^3+27x^2-16x-21

[bettyboop22]

given that x^6-7x^4+16x^3+27x^2-16x-21
has -1 as a zero of multiplicity 2
1 as a single zero
-3 as a single zero
find all other zeros

I also need help with this probem:
Find the 6 zeros (real and imaginary) of f(x)=x^6-64

 

[Loren]

Re: help finding other zeros

You don't see the difference between two squares, which leads directly to two real roots and 4 complex?

 

[Deleted member 4993]

Re: help finding other zeros

given that x^6-7x^4+16x^3+27x^2-16x-21
has -1 as a zero of multiplicity 2 <<< That means (x+1)[sup:3cauknxa]2[/sup:3cauknxa] is a factor of the given function.
1 as a single zero<<< That means (x-1) is a factor of the given function.
-3 as a single zero<<< That means (x+3) is a factor of the given function.
find all other zeros

so then

x^6-7x^4+16x^3+27x^2-16x-21 = (x+1)[sup:3cauknxa]2[/sup:3cauknxa] * (x-1) * (x+3) * f(x)

What is the degree of f(x) [i.e. the highest power of x in f(x)]?

What is f(x)? - one of the ways to find that would be to use long or synthetic division.

Finally, find zeroes of f(x).

I also need help with this probem:
Find the 6 zeros (real and imaginary) of f(x)=x^6-64