Your Practice Set – Applications and Interpretation for IBDP Mathematics
23
Paper 1 – Complex Roots of Quadratic Equations
Example
A quadratic function is given by { y: y� 49 }.
2 f ( x) � x �6x
� 58 . It is given that the range of f( x ) is
( a ) Explain why there is no real root for the equation f( x) � 0 .
( b ) Find the complex roots of the equation f( x) � 0 a� bi , where a , b� .
[ 1 ]
, giving the answer in the form
[ 3 ] ( c ) If the above two complex roots are located on an Argand diagram , write down the distance between the roots . [ 1 ]
Solution
( a ) The range of f( x ) is { y: y� 49 }, means the graph
( b ) of f( x ) does not have any x -intercept. x
2
�6x�58 � 0
2
�( �6 ) � ( �6 ) � 4 ( 1 )( 58 ) x � ( A1 ) for substitution
2 ( 1 )
6 � �196 x � ( A1 ) for simplification 2
R1
6 � 196i x �
2 x �3� 7i
A1
( c ) 14 A1
[ 1 ]
[ 3 ]
[ 1 ]
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