Question

Find a third degree polynomial that has zeros at x=-1,1, and 2. whose x term has coefficient 3.
help!? Ill give out medals!

Answer 1

it will be of the form

a(x+1)(x - 1)(x - 2)

where a is a constant

Answer 2

really? because for like a 4th degree one where x=0,1,-1, and -2 and the x^2 term has coefficient of 5. the answer is : -5x^4-10x^3+5x^2+10x.. Im pretty confused..

Answer 3

oh is that the form and then i just put the constant in front and it will get an answer?

Answer 4

expanding we get

a(x + 1)(x^2 - 3x + 2)
= a( x^3 - 3x^2 + 2x + x^2 - 3x + 2)
= a(x^3 -2x^2 - x + 2)

this should help

Answer 5

... ugh i know im probably being stupid or something, but im on no sleep. So just asking.. what is this? Is that the answer? an equation i use to get the answer?..

Answer 6

@cwrw238 ?

Answer 7

sorry - I was called away

Answer 8

oh.

Answer 9

right so the coefficient of x must be 3 - that makes a = 3

so you have to multiply each term in the brackets by 3 and you have your polymimial

Answer 10

* polynomial lol

Answer 11

oh, ok. lol. Thanks a lot!. can i ask you 1 more question?

Answer 12

ok

Answer 13

so i have to find the possible rational zeros for x^4-4x^3+3x^2+4x-4. I think those are +-1, 2, and 4. Then i have to factor it. So i guess i just try them out to see which ones work and then factor?

Answer 14

they look right - because the last term is -4
yes just check them out first

Answer 15

ok. but question.. for another problem earlier which ended in -3 and the first erm was 2. The zero's were ony 1,-1/2, and -3. Not +- 1,3, -3/2, or /1,2. Why did some just dissapear. And then the polynomial ends up being factored by x-1 which i thought should be x+1?

Answer 16

not all the factors are necessarily zeros
if one zero is 1 then it will be divisible by x - 1 (that's the Factor Theorem)

Answer 17

oh. so if it was -1 it would be x+1?

Answer 18

yes

Answer 19

I checked out -1,1 and 2 for your other equation and they fit OK

Answer 20

yea, i was checking them now actually. Was on 4. lol

Answer 21

I literally have this class in about 20 minutes so If you could help with 1 more question...I got another one. like the one we did before though my signs were messed up. But what would be the equation for this: 5th degree. zero of multiplicity 2 at x=1, zero at x=4 and factor of x^2+x+1? that one just i have no idea.

Answer 22

4 does not fit -according to me

Answer 23

maybe 2 is a repeat root
in which case the factors are
(x+1)(x-1)(x-2)^2

Answer 24

yes 2 is a repeated root

Answer 25

so for the 5th degree one. that is the equation? and i just solve that?

Answer 26

oh yea. I see that.

Answer 27

wow. ok. I think i actually get this stuff now. :)

Answer 28

is best stated as multiplicity 2 not repeated as I did

Answer 29

yea. I am squaring the final answer though right? after i distribute each one..

Answer 30

yes

Answer 31

gotta go right now sorry

Answer 32

its ok. you helped alot! thanks so much!! Yea, and i got x^3-2x^2-x+2 and then square that and i should be set. Thanks again!