Analysis and Approaches for IBDP Maths Ebook 2 | Page 35

8
Example
Paper 1 Section A – Sum and Product of Roots
2
The equation
x � x � x � � k has roots r 1
, r 2
and r 3
. Given that
3 2
3 24 5
r1 � r2 � r3 � rr
1 2r3
, find the value of k .
[5]
Solution
3 2
3 24 5
x � x � x � � k
3 2
3x 24 x x (5 k) 0
� � � � � (M1) for valid approach
r1 � r2 � r3 � rr
1 2r3
24 5 � k
�� � � M1A2
3 3
24 �5�
k
k �� 19
A1
[5]
Exercise 8
1. The equation
1 2 2 3 1 3 1 2 3
� � � � � has roots r 1
, r 2
and r 3
. Given that
3 2
2x 30x kx 20 x 5
rr � r r � rr � 2rr r , find the value of k .
2. The equation
4 3 2 4 3
x � kx �3x � 2x �1� �x � 4x
� 13 has roots r 1
, r 2
, r 3
and r 4
. Given
that rr 1 2
r 3
r 4
� r 1
� r 2
� r 3
� r 4
� 0 , find the value of k .
[5]
[5]
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