Question

show the root x4-12x-5=0 given that -1+2i in a root​

Answer 1

Answer:Solve x^4 - 12x - 5 = 0 given that -1 + 2i is a root.

I’ve used synthetic division to get the answers x = 1 +/- 2i , 1 +/- sqrt 2

I’ve having trouble checking the answers though because of that imaginary number. How can I check these kind of problems?

If (-1+2i) is a solution, its complex conjugate (-1-2i) must be a solution.

In other words

x = -1+2i

x = -1-2i

are solutions

so

x+1-2iand x+1+2i are both factors

so their product should be a factor

I get x^2+2x+5

now do your division

I get

x^2-2x-1

well

that is

(x-1)(x-1)

so my four solutions are those two complex conjugates and x=1 and x =1 again

Step-by-step explanation:

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