Question

Find a polynomial function that has the given zeros.

Answer 1

1 + sqrt3, 1 - sqrt 3

Answer 2

a polynomial has a zero at \(x=a\) iff \(x-a\) is a factor of the polynomial

Answer 3

so to make a polynomial that has two zeroes, x=a and x=b, the factors should be\[(x-a)(x-b)\]

Answer 4

Yeah, I understand how to do them, I'm just really confused on when I'm looking a function with a zero with a square root involved

Answer 5

in your case \[a=1+\sqrt2\]and\[b=1-\sqrt3\]so what are your factors?

Answer 6

Is my answer just going to be f(x)= (-1 - sqrt3)(-1 + sqrt3) ?

Answer 7

what happened to x ?
o_O

Answer 8

...and no, you probably should multiply it out anyway... once it's set up right that is

Answer 9

Yeah, I'll multiply it. I just don't know how to set it up right. 3:

Answer 10

(x-a)(x-b)=?
sub in for a and b

Answer 11

f(x) = (x + 1 - sqrt3) (x + 1 + sqrt3)?

Answer 12

and multiplied out, which I will do if I know this is right.

Answer 13

not quite...

Answer 14

(x-a)(x-b)=[x-(1+sqrt3)][x-(1-sqrt3)]=?

Answer 15

So I just needed to add the extra parentheses..?

Answer 16

you messed up with the +/- stuff, gotta be more careful
I set it up for you so all you have to do is simplify

Answer 17

Thank you so much!!!!!! :)

Answer 18

welcome!