Question

if x^2+px+1 is a factor of the expression ax^3+bx+c
a.a^2+c^2=-ab
b.a^2-c^2=-ab
a^2-c^2=ab

Answer 1

@RadEn pls..hlp

Answer 2

what's the question here ?

Answer 3

this is the question

Answer 4

What is "the factor of the expression"? Sorry, my English is not so good.

Answer 5

ax^3+bx+c is any expression and x^2+px+1 is factor of it that's what ques says

Answer 6

Thank you, I get it.

Answer 7

lets try
whats sum , product of roots for x^2+px+1 ?
and whats for that cubic expression ?

Answer 8

sum is -p and product is 1

Answer 9

sum for cubic expression is 0 and product is c

Answer 10

product is ? c? no...

Answer 11

bt why

Answer 12

ok, so let 3 roots of cubic exp be A,B,C
product of roots for cubic expression ax^3+bx^2+cx+d is -d/a , right ?

Answer 13

so, here. won't it be -c/a ?

Answer 14

k...i undrstand it

Answer 15

so,
since x^2+px+1 is a factor of the expression ax^3+bx+c,
two from A,B,C are also roots of x^2+px+1
got this ? this is important step

Answer 16

let that 2 roots be A,B

Answer 17

kk...

Answer 18

so, now we have
AB =1
A+B=-p

ABC=-c/a
A+B+C =0
what about AB+BC+CA =...?

Answer 19

that's simply b

Answer 20

not b/a ?

Answer 21

http://www.mathsisfun.com/algebra/polynomials-sums-products-roots.html

Answer 22

oh sorry i m considering a=1

Answer 23

then wt shud we do now

Answer 24

don't.
so,
AB =1
A+B=-p

ABC=-c/a
A+B+C =0
AB+BC+CA =b/a

everything clear till here ?
see if you get C=p or not.....

Answer 25

yaa c=p

Answer 26

also fro ABC = -c/a
since AB=1
C=p=-c/a
ok?

Answer 27

yaa i got it uptill here

Answer 28

good.
AB+BC+CA =b/a
1 + C (A+B) = b/a
got this ? as AB=1

Answer 29

yaaaa

Answer 30

now just plug in values!
C = p = -b/a
A+B = -p = b/a

Answer 31

c=p=-c/a then hw it came c=p=-b/a

Answer 32

thats why i took capital c ---->C to avoid confusion

C = p
not c=p

Answer 33

no no i m saying dat C=p=-c/a and u r getting it as C=p=-b/a

Answer 34

and my bad, typing mistake
C = p = -c/a

Answer 35

sorry

Answer 36

it's jst ok...

Answer 37

C = p = -c/a
A+B = -p = c/a

Answer 38

1-c^2/a^2 = b/a
....