# Roots of a squared polynomial ( complex numbers)

1. Apr 3, 2014

### Axe199

1. The problem statement, all variables and given/known data

problem in a pic attached

2. Relevant equations

3. The attempt at a solution
i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got really confused and now i dont know what he wants from me

File size:
10.4 KB
Views:
91
File size:
23.2 KB
Views:
88
2. Apr 3, 2014

### Ray Vickson

He wants you to tell him what are all the square roots of -2, -2+2*sqrt(3)*i and -2 - 2*sqrt(3)*i.

3. Apr 3, 2014

### Axe199

why cant i just say (z+2)^2= 0 and solve and do the same for the complex roots?
why do i have to find the roots of the -2?

4. Apr 3, 2014

### slider142

(z + 2)2 is not a factor of p(z2). It is a factor of (p(z))2, however, a completely different polynomial.
The polynomial is not the object being squared. p(z2) only means that the variable z is being replaced with the variable z2. So, as a result, we know that z2 + 2 is a factor.

5. Apr 3, 2014

### Axe199

okay...thanks very much, tht was a tricky one, or maybe i am stupid :D
either way , thanks , i got it