Question

Find a cubic function with the given zeros.

Answer 1

\[\sqrt{2}\] \[\sqrt{-2}\]
-2

Answer 2

not really possible with real coefficients

Answer 3

could it be \(2,-\sqrt{2}\) and \(\sqrt{2}\) ?

Answer 4

Yes, that's it

Answer 5

$$(x-2)(x+\sqrt{2})(x-\sqrt{2})$$

Answer 6

i did since presumably this is not a class in functions of a complex variable

Answer 7

your job is to write in factored form as \((x-2)(x+\sqrt{2})(x-\sqrt{2})\) and then multiply out
the last two are easiest, you get \((x-\sqrt{2})(x+\sqrt{2})=x^2-2\)
so finish by multiplying
\[(x-2)(x^2-2)\]

Answer 8

btw was the zero \(2\) or \(-2\) ?

Answer 9

if it is \(-2\) as you wrote in the first one, then you should multiply
\[(x+2)(x^2-2)\]
you good with that?

Answer 10

What would that come out to be?

Answer 11

before we do it, lets make sure we have the zeros correct
is one of them \(2\) or is one of them \(-2\) ?

Answer 12

$$x^3-4$$

Answer 13

definitely not \(x^3-4\)

Answer 14

i just multiplied out your two binomials

Answer 15

lol

Answer 16

lets get the zeros correct and then we can do it, because otherwise we will not get it right

Answer 17

-2

Answer 18

if the zeros are \(-2,\sqrt2,-\sqrt2\) then we need to multiply
\[(x+2)(x^2-2)\]

Answer 19

ok got it

Answer 20

you have to do 4 multiplications
\[(x+2)(x^2-2)=x^3+2x^2-2x-4\]

Answer 21

sometimes know by the unfortunate mnemonic devise of "foil" but it is really the distributive property

Answer 22

yes, i know it as foiling. thank you!

Answer 23

not sure where the \(x^3-4\) comes from though

Answer 24

yw