Write a polynomial function of the least degree that has real coefficients, the given zeros, and a leading coefficient of 1 (Write your answer in standard form)
x=4,2i,-2i

Question

Write a polynomial function of the least degree that has real coefficients, the given zeros, and a leading coefficient of 1 (Write your answer in standard form)
x=4,2i,-2i

ganeshie8 · Answer

hint : complex roots come in pairs

ganeshie8 · Answer

thats a pretty useless hint :/
already you're given pair of zeroes lol

mathmale · Answer

Indeed.  Root 2i corresponds to factor (x-2i); root -2i corresponds to (x+2i).  Root 4 corresponds to what factor?  What next in the sol'n of this problem?

@ganeshie8:  You're forgiven (this time only).  :)

ganeshie8 · Answer

:)

mathmale · Answer

Cool-1:  would you please multiply together (x-2i) and (x+2i)?  What do you get?

anonymous · Answer

(x^2+4)?

anonymous · Answer

so (x-4) (x^2+4)

anonymous · Answer

= X^3-4x^2+4x-16

mathmale · Answer

I haven't checked every detail, but it appears that you're doing exactly the right thing.  Note that the "leading coefficient" is 1:

$$1x^3$$has the coeff. ' 1 ' and thus satisfies that particular requirement.

mathmale · Answer

Cool, Cool-1!  Looks like you're making very good progress.