Analysis and Approaches for IBDP Maths Ebook 2 | Page 36

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. Let
3 2
f ( x) � 6x �18x �36x
� 72 , x� . r 1
, r 2
and r 3
are the roots of f( x) � 0 .
(a) Find the value of
1 1 1
� � .
r r r r r r
1 2 2 3 1 3
A new polynomial is defined by g( x) � f ( x � 3) .
[4]
(b) Find the sum of the roots of the equation gx� ( ) 0 .
[2]
4. Let
3 2
g( x) � �x � 71x �10x
� 15, x� . r 1
, r 2
and r 3
are the roots of gx� ( ) 0 .
(a)
Find the value of
1 1 1
� � .
r r r
1 2 3
A new polynomial is defined by h( x) � 2 g( x)
.
(b) Find the product of the roots of the equation hx ( ) � 0.
[4]
[2]
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