Question 747996: Find the polynomial equation with integral coefficients that has the given roots: -2, i, -i.
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! Find the polynomial equation with integral coefficients that has the given roots: -2, i, -i
It's a matter of solving it backwards. You start
with three equations with x equaling to them:
x=-2, x=i. x=-i
Get 0 on the right of each of these because that
would have been the next to last step of solving
the equation:
x+2=0, x-i=0, x+i=0
Before that was the zero factor principle, so to
reverse that we multiply all three equation together
(x+2)(x-i)(x+i) = 0
(x+2)(x²-i²) = 0
Then use the fact that i² = -1
(x+2)(x²-(-1)) = 0
(x+2)(x²+1) = 0
x³+x+2x²+2 = 0
Putting the terms in descending order:
x³+2x²+x+2 = 0
Edwin
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