Exercise 23
1 . A quadratic function is given by
is { y: y�� 25 }.
2 f ( x) � �x � 4x � 29 . It is given that the range of f( x )
( 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 ]
2 . A quadratic function is given by f x
2
( ) ( x 5 ) 64 � � � .
6
( 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 ]
3 . A quadratic function is given by f( x) � 0 are 4 � 13i and 4 � 13i .
( a ) Write down the values of
( i ) ( 4 �13i ) � ( 4 � 13i ) ;
2 f ( x) ax bx c � � � . It is given that the complex roots of
( ii ) ( 4 �13i )( 4 � 13i ) .
( b ) Hence , find the expression of f( x ), giving the answer in terms of a .
The graph of f( x ) passes through ( 4,169 ) .
[ 2 ]
[ 3 ]
( c ) Find the value of a .
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