find zeroes of x^3+3x^2+ix+(4+i); factor x^4-x^2-20

[Loserface]

i cant do this one. we are learning about finding zeros. I dont which method I should use for this problem:

if i is a zero of x^3+3x^2+ix+(4+i) find the rest of the zeros

what do i do? synthetic divison? or long division?

when i did long division i got a werid polynomial with a lot of 'i's in them what do I do with that?

also: i cant seem to figure this out, i tried synthetic it didnt really work....

factor x^4-x^2-20 over real and complex numbers

can anyone help? thanks.

 

[daon]

Re: Finding Zeros over complex and real numbers

If i is a zero, either use synthetic dicision or long division to obtain a quadratic times a linear factor. Then use the quadratic formula. Unfortunately polynomials over C don't need complex roots to come in conjugate pairs.

For the second, let t=x^2. then you have the polynomial t^2-t-20.