Complex number

Mar 2010
26
0
Malaysia
Question is find all the roots :
z^4 + 2z^3 + 5z^2 + 8z + 4 = 0

I"m stuck at the beginning of this question. But i knew how to do this type of question and only does not know how to start.
Thanks.
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
Question is find all the roots :
z^4 + 2z^3 + 5z^2 + 8z + 4 = 0

I"m stuck at the beginning of this question. But i knew how to do this type of question and only does not know how to start.
Thanks.
1. By trial and error you can see that z = -1 is a root of the equation. (Actually z = -1 is a double root of the equation) Use long division to get the remaining terms.

\(\displaystyle z^4 + 2z^3 + 5z^2 + 8z + 4 = 0~\implies~(z+1)^2 \cdot (z^2+4)=0\)

2. Go on!
 
Mar 2010
26
0
Malaysia
I cant go on to next step...

Before that i done this question
z^4 + 2z^2 + 4 = 0

Let x = z^2

x^2 + 2x + 4 = 0

a = 1 , b = 2, c = 4

x = -b sqr b^2 -4ac / 2a

then i can get the answers.
 
Similar Math Discussions Math Forum Date
Calculus
Advanced Algebra
Algebra
Algebra