Let-A-x-is-a-cubic-polynomial-and-B-x-x-1-x-2-x-3-Find-how-many-C-x-so-that-B-C-x-B-x-A-x-

Question Number 21656 by Joel577 last updated on 30/Sep/17

Let A (x) is a cubic polynomial and B (x) = (x - 1) (x - 2) (x - 3)

Find how many C (x) so that

B (C (x)) = B (x) . A (x)

Commented by Joel577 last updated on 01/Oct/17

T h e a n s w e r {i s n}^{'} t g i v e n t o m e .

P l s e x p l a i n, S i r

Commented by alex041103 last updated on 30/Sep/17

{I s n}^{'} t i t 3 ?

Commented by alex041103 last updated on 01/Oct/17

I^{'} m n o t e x a c t l y s u r e b u t \dots h e r e i t i s .

F o r s h o r t l e t m e p u t A (x) . B (x) = A B

a n d C (x) = C

\Rightarrow B (C) = A B

(C - 1) (C - 2) (C - 3) = A B

C^{3} - 6 C^{2} + 11 C - 6 = A B

C^{3} - 6 C^{2} + 11 C - (6 + A B) = 0 = P (C)

A n d b e c a u s e P (C) i s a c u b i c p o l i n o m i a l

i n t e r m s o f C, t h e n a s s t a t e d i n t h e

F u n d a m e n t a l t h e o r e m o f A l g e b r a,

f o r C t h e r e a r e t h r e e s o l u t i o n s (r e a l

a n d c o m p l e x) .

T h e s o l u t i o n s w i l l b e i n t e r m s o f A (x) . B (x)

\Rightarrow C w i l l b e a f u n c t i o n o f x

\Rightarrow T h e r e a r e t h r e e C (x) t h a t s a t i s f y

B (C (x)) = A (x) . B (x)

Commented by Joel577 last updated on 01/Oct/17

b u t t h e o p t i o n s a r e

19

22

24

27

32

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