Analysis and Approaches for IBDP Maths Ebook 2 | Page 39

10
Example
Paper 2 Section A – Number of Solutions
2
Find the values of r such that the equation
solutions.
3 2
x x x r
�6 �9 � � 3 has two distinct real
[4]
Solution
3 2
x x x r
�6 �9 � � 3
3 2
x 6x 9x 3 r
� � � � (M1) for valid approach
By considering the graph of
3 2
y x x x
� �6 �9 � 3, the local
maximum is (1, 7) and the local minimum is (3, 3) .
Thus, r � 3 or r � 7 . A2
(M1) for valid approach
[4]
Exercise 10
1. Find the range of values of r such that the equation
distinct real solutions.
2. Find the range of values of k such that the equation
solution.
3. Find the range of values of r such that the equation
distinct real solutions.
4. Find the range of values of k such that the equation
distinct real solutions.
� � � � � � has three
3 2
2x 3x 12x r 7 0
4 3 2
x 8x 16x k 4x
� � � � has no real
[4]
[4]
2
2 r�
24x
x �180
� has at most two
x
2 4
8 x (2x �1) � k �192x � x has four
[4]
[4]
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