I have some problems to do and could use some help. It's all about polynomials and complex numbers, and I basically just started the topic and don't have too much of a clue about it. Any help would be appreciated, but if you could give me some explanations of what to do, how to do it and why to do it, that would be really great.
#1 |(x/(8-x)] <= 2 I need to find the exact values for x. Unfortunately I never had inequalities. Please help me with this.
#2 This one is very hard, please help me with it. x³-x+1=0 has the roots a and b, I need to show that x³+x²-1=0 has the root ab. I also got the hint that I should use x³-x+1=(x-a)(x-b)(x-c) but that doesn't help me too much.
#3 |z+16| = 4|z+1| I need to find |z| if z is a complex number
#4 I need to find the cube roots of -27.
Thank you very very much.
Regards and best wishes,