Knowing that 2i is one answer to the equation x^4 - 2x^3 + 6x^2 - 8x + m = 0, find the 'm' and the other possible answers.
1 answer:
Ok so remember
if a+bi is a root, then a-bi is also a root
since 2i is a root, -2i is also a root
use synthetic division and the fact that when we divide by 2i and -2i, we have to get all real coeficients and end witha zero at the end
I will show the division in the attachment
we find m=8
we then find th resulting equation that is x^2-2x+2=0
quadratic formula
x=
x=1+i or 1-i
m=8 and the other roots are
x=-2i, 1+i, 1-i
if a+bi is a root, then a-bi is also a root
since 2i is a root, -2i is also a root
use synthetic division and the fact that when we divide by 2i and -2i, we have to get all real coeficients and end witha zero at the end
I will show the division in the attachment
we find m=8
we then find th resulting equation that is x^2-2x+2=0
quadratic formula
x=
x=1+i or 1-i
m=8 and the other roots are
x=-2i, 1+i, 1-i
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