# Complex number

#### wkn0524

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
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!

#### wkn0524

Sure, trying now #### wkn0524

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.

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