SOLUTION: Consider a polynomial equation of z^4 - z^3 - 5z^2 - z - 6 = 0 . i. Show that z = -i is a root of the polynomial equation. ii. Write its conjugate root. iii. Find the other two

Question 285095: Consider a polynomial equation of z^4 - z^3 - 5z^2 - z - 6 = 0 .
i. Show that z = -i is a root of the polynomial equation.
ii. Write its conjugate root.
iii. Find the other two roots.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
i. -plug in -i for z and see if it works.
ii-complex roots come in pairs one positive and one negative so i should also work.
iii-(x-i) and (x+i) are factors so (x^2-1) is a factor
divide z^4 - z^3 - 5z^2 - z - 6 = 0 by (x^2-1) to find the other factors
z^2-z-6 factors into (z-3) (z+2) and so the other roots are 3 and -2

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