Analysis and Approaches for IBDP Maths Ebook 1 | Page 19

4
Example
Paper 1 Section A – Find the unknown
coefficients of a quadratic equation
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2
Solution
The equation
k .
2
kx k x
� ( �3) �3 � 0 has two distinct real roots. Find the possible values of
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2
� � b � 4ac
(M1) for discriminant
2
b �4ac
� 0
R1
2
( k�3) � 4( k)( �3) � 0
(A1) for substitution
2
k k k
2
�6 �9�12 � 0
k � 6k� 9 � 0
A1
2
( k �3) � 0
(M1) for factorizing
k �3� 0 or k �3� 0
A1
k �� 3 or k �� 3
A2 N4
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Exercise 4
1. The equation
2 2
x �5x � k � 0 has two equal real roots. Find the values of k .
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2. The equation
2
x kx k
� 4 � 2 � 0 has two distinct real roots. Find the possible values of k .
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3. The equation
4. The equation
x
2
�1 � (1 � k)
x has no real root. Find the possible values of k .
2
4 x (4k 16) x 25k
0
� � � � has real roots. Find the possible values of k .
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