Question

http://imgur.com/hgKNzJl
Can i get some help?
So far I've figured out the real Zeros and multiplicity... (x+2)(x+1)^2(x-1)
but i dont know how to figure out the rest for the question..

Answer 1

@Nnesha
Any idea?

Answer 2

Note that the general equation with 4 given roots is
f(x)=a(x-x1)(x-x2)(x-x3)(x-x4)
In the case of x1=-2, x2=x3=-1, x4=1
so
f(x)=a(x+2)(x+1)^2(x-2)
is correct.
The value of a can be matched by

1. The product a(x1)(x2)(x3)(x4) must equal the y-intercept, which is -4 for the given problem. This allows you to solve for the value of a.
2. the concavity of the polynomial. In the case of concave upwards, then the leading coefficient (=a) must be >0. Conversely, if the curve is concave downwards, then the leading coefficient is <0.
This will check whether the sign of "a" calculated in (1) above is correct.

Answer 3

Ahh, so now i'd solve for A by inputting 4 into the equation?

Answer 4

read first step :)

Answer 5

substitute f(x) which is same as y for -4
as mentioned above in first step
set the equation equal to y-intercept (when x =0)
and the y-intercept for this question is -4

Answer 6

thank you ^_^

Answer 7

o^_^o

Answer 8

@Nnesha just to amke sure, A = 2 then?

Answer 9

hmm i didn't get that

Answer 10

U sure? cuz i just multiplied it out w/ a=2 and it came out with -4 as the constant coeffiecent which would mean my equation is right, right?

Answer 11

@Nnesha

Answer 12

yes i'm here
not gonna die :D

Answer 13

yes i didn't get 2

Answer 14

I might :O Things happen.
What'd you get?
-4=a(0+2)(0+1)^2(0-1)
-4=-2a

Answer 15

that's what math posted above
f(x)=a(x+2)(x+1)^2(x-2)
substitute y for -4 and all x's for 0

Answer 16

ohhh math, that was an example
let me look at the original questioin :P

Answer 17

oh lol XD

Answer 18

ye looks good

Answer 19

thx

Answer 20

hmm

Answer 21

yus?

Answer 22

opps nvm
i was checking the answer
so i forgot to distribute (x+2)(x-1)(x+1)^2 by 2 xd

Answer 23

ah XD np

Answer 24

*\(f(x)=a(x+2)(x+1)^2(x-\color{red}{1})\)
Sorry, my bad!

Answer 25

it's okay! :)
nice explanation btw!

Answer 26

Thank you! :)