Analysis and Approaches for IBDP Maths Ebook 2 | Page 125

38
Paper 2 Section A – Complex Roots of Polynomials
Example
(a)
(b)
(c)
Show that the complex number i is a root of the equation
Find the sum of roots of this equation.
Find the other roots of this equation.
3 2
x x x
�3 � �3 � 0.
[2]
[2]
[4]
Solution
(a)
(b)
(c)
3 2
i 3i i 3
� � � M1
� �i �3( �1) �i � 3
A1
� �i �3�i � 3
� 0
Thus, i is a root of the equation.
AG
The sum of roots
�3
��
1
A1
� 3
A1
The second root is � i .
A1
Let a be the third root.
�3
a � i � ( �i)
� � M1A1
1
a � 3
Thus, the third root is 3.
A1
[2]
[2]
[4]
9
www.seprodstore.com
115