Analysis and Approaches for IBDP Maths Ebook 2 | Page 126

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 38
1. (a) Show that the complex number � i is a root of the equation
(b)
(c)
2. Let
a�
bi
4 3 2
x x x x
�8 �13 �8 �12 � 0 .
Find the product of roots of this equation.
Find the other roots of this equation.
3 2
P( z) � z �12z � 49z
� 68 , where z � . Two of the roots of Pz ( ) � 0 are 4 and
�
, where a , b� . Find the values of a and b .
[2]
[1]
[5]
[6]
4 3 2
3. Let P( z) � z �14z �98z � 406z
� 841, where z � . Two of the roots of Pz ( ) � 0 are
�
a� bi and b�
ai
, where a , b� and a� b. Find the values of a and b .
[8]
4. Let
P x � x � x � x � x � be a quartic polynomial such that the equation
4 3 2
( ) 16 97 300 468
�
Px ( ) � 0 has a complex root a�
bi
, where a , b� . The graph of y � P( x)
has the
x -axis as a tangent at (6, 0) . Find the values of a and b .
[7]
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