Question

-1+i is a root of x^4+4x^3+5x^2+2x+k=0 then the other roots are?​

Answer 1

Explanation:

I hope you will understand

Answer 2

Answer:

Explanation:

x^4–4x³+8x+3=0

After a little trial and error, you will notice that x=3 is one answer. Then, if this is so, then x-3 is a factor. So:

x^4–4x³+8x+3/(x-3)=x³-x^2–3x-1

Now, x³-x²-3x-1=0 can be solved with x=-1. Thus, it follows that x+1 is a factor of this. So:

x³-x²-3x-1/x+1=x²-2x-1

Then:

x²-2x-1=0

x²-2x=1

x²-2x+1=2

(x-1)²=2

x-1=√2

x=1±√2

So the four roots of this equation are:

x=3, -1, 1+√2, 1-√2 ………………..