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Paper 1 · November 2018 · Complex Numbers

The equation $x^3 - 2x^2 + 4x - 8 = 0$ has a root $x = 2i$ . Find the other two roots.

A

x = -2i

and

x = 2

B

x = -2i

and

x = -2

C

x = 2i

and

x = 2

D

x = -2i

and

x = 4

Explanation

Complex roots occur in conjugate pairs, so

x=-2i

is a root and

x^2+4

is a factor. Then

x^3-2x^2+4x-8=(x-2)(x^2+4)

, giving the third root

x=2

.

Derived from ZIMSEC Mathematics Paper 1, November 2018, Q1

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