Analysis and Approaches for IBDP Maths Ebook 2 | Page 29

Chapter
2
2
Polynomials
SUMMARY POINTs
�
Number of roots of the polynomial
The maximum number of roots of f( x) � 0 is n
n
f ( x)
� a x � a x � � a x � a x � a :
n
n�1 2
n�1 2 1 0
�
Sum and product of roots of
1. r , 1
r
2
, …, r n
: Roots
an�
1
2. r1� r2
� � rn
� �
a
n
n
f ( x)
� a x � a x � � a x � a x � a :
n
n�1 2
n�1 2 1 0
an�2
3. rr
1 2
� rr
1 3
� � rr
1 n
� r2 r3 � r2 r4 � � r2 rn � � rn �1rn
�
a
…
a0
4. r1 r2 r3 r
1
( 1) n
n� rn
� �
a
n
n
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