Question

Please help:)
The value of a & b so that \[\LARGE{\color{green}{x^3+ax^2+bx+6}}\] is divisible by (x+1) & (x-2) are???
@jim_thompson5910 :)

Answer 1

(x+1)(x-2) = x^2 - x - 2


So if x^3+ax^2+bx+6 is divisible by x^2 - x - 2

Then x^3+ax^2+bx+6 = (x+k)(x^2 - x - 2)

For some value of k

Expand to get...


x^3+ax^2+bx+6 = (x+k)(x^2 - x - 2)

x^3+ax^2+bx+6 = x(x^2 - x - 2) + k(x^2 - x - 2)

x^3+ax^2+bx+6 = x^3 - x^2 - 2x + kx^2 - kx - 2k

x^3+ax^2+bx+6 = x^3 - x^2+ kx^2 - 2x - kx - 2k

x^3+ax^2+bx+6 = x^3 + ( -1 + k)x^2 + (-2x - k)x - 2k


Do you see where to go from here?

Answer 2

oops made a typo in the last line, it should be

x^3+ax^2+bx+6 = x^3 + ( -1 + k)x^2 + (-2 - k)x - 2k

Answer 3

wht is k here?? @jim_thompson5910

Answer 4

Notice the constant on the left side is +6

Answer 5

The constant on the right side is -2k

Answer 6

k in ur first reply:)

Answer 7

not sure what you mean

Answer 8

why did u take this k & from where??

Answer 9

oh I just introduced another variable k...well it's actually a constant

Answer 10

Because it states that x^3+ax^2+bx+6 is divisible by x^2 - x - 2

Which means that

(x^3+ax^2+bx+6)/(x^2 - x - 2) = x+k

and then I rearranged terms

Answer 11

ok then plz solve further i m so confuse for this question

Answer 12

The constants on both sides are equal so

6 = -2k

Answer 13

so wht the value of a & b??

Answer 14

What is the value of k?

Answer 15

-3

Answer 16

So from x^3+ax^2+bx+6 = x^3 + ( -1 + k)x^2 + (-2 - k)x - 2k, we see that

a = -1 + k

and

b = -2 - k

Answer 17

Answer:-
a=-4
b=-1

Answer 18

correct??

Answer 19

a is correct, b is not

Answer 20

sorry 1
made a typo

Answer 21

good a = -4 and b = 1

Answer 22

thank u:)
have a nice day

Answer 23

you're welcome