Question

the expression ax^3-8x^2+bx+6 is divisible by x^2-2x-3.Find the values of a and b.

@eric_d

Answer 1

say `g(x) = x^2-2x-3`

we're given `g(x)` divides the given expression,
so can we say that the individual factors of `g(x)` also divide the given expression ?

Answer 2

*

Answer 3

ok..

Answer 4

can you factor `g(x)` ?

Answer 5

(x-3)(x+1)

Answer 6

Excellent ! that means `x-3` and `x+1` are factors of given expression, right ?

Answer 7

ys

Answer 8

i dnt know how u manage that much of question :-\

Answer 9

i dnt know how u manage that much of question

Answer 10

You mean Ganesh ?
@ikram002p

Answer 11

hehe , yeah :P

Answer 12

:P

Answer 13

good :) so we appeal to factor/remainder theorem :
if `x-a` is a factor of f(x), then `f(a) = 0`

Answer 14

ok..

Answer 15

Well isn't this like saying if we have the number 72 and I tell you it is divisible by 6 does this mean that 72 is also divisible by 3 and 2?

Answer 16

yep the same kai

Answer 17

exactly ^^ @eric_d thats a very good analogy to see why the factors of `f(x)` must also divide the given expression

Answer 18

since `x-3` and `x+1` are factors of given expression also, can we use factor/remainder theorem and get two equations in a and b ?

can you try ?

Answer 19

sure

Answer 20

27a+3b-66 .....1
-a-b+2 ......2
like this

Answer 21

Perfect !

Answer 22

two equations and two unknowns,
not very exciting, anybody can solve them :)

Answer 23

When solving simultaneously,
I'm getting a=2.5
??

Answer 24

isolved the question in defferent way , but i got 3
mmm which make no sense cuz this way is correct as well

Answer 25

You can show ur working here

Answer 26

is b = 13 ?

Answer 27

the given answer is b=-5

Answer 28

ok this is what i did

Answer 29

@eric_d there is a small typo in ur equations which ive overlooked earlier :
27a+3b-66 =0.....1
-a-b\(\color{Red}{-}\)2 =0 ......2

solving gives you
http://www.wolframalpha.com/input/?i=solve+27a%2B3b-66%3D0%2C-a-b-2%3D0

Answer 30

hehe perfect xD

Answer 31

So, I can't solve the eqn simultaneously

Answer 32

@ikram002p

Answer 33

-a-b=2
27 a +3b =66

mmm xD

-3a-3b =6
+
27 a+3b =66
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24a=66+6=27

mmm u know find a

Answer 34

Okay

Answer 35

Understood..
Thank you @ganeshie8 @ikram002p @Kainui

Answer 36

sorry i made to many typo xD
66+6= 72

Answer 37

It's alrite