Write a po

Question

Write a po

iwanttogotostanford · Answer

@TheSmartOne @zepdrix @sweetburger please help ,e

zepdrix · Answer

Complex roots always come in conjugate pairs.
So if 1+3i is a root, then 1-3i is also a root of this polynomial.
So our minimal degree polynomial will be degree 4 with these four roots.

iwanttogotostanford · Answer

and i know the first part of it will be x^4 but then It will be -3x^3 right?

zepdrix · Answer

I don't think you can shortcut like that.
You have to construct the polynomial from the factors which give you your roots.

Since 2 is a root, it tells us that (x-2) is a factor of this polynomial.
Since -4 is a root, it tells us that (x+4) is a factor.
Since 1+3i is a root, it tells us that (x-1-3i) is a factor.
Since 1-3i is a root, it tells us that (x-1+3i) is a factor.

So your polynomial will be,$$\large\rm (x-2)(x+4)(x-1-3i)(x-1+3i)$$

zepdrix · Answer

And you'll expand all of that out,
and combine like-terms.

zepdrix · Answer

I think there is an easier way to multiply out the complex part.. I can't seem to remember the trick though..

zepdrix · Answer

Yes that's correct.
Looks like there is no x^3 in this one :)

iwanttogotostanford · Answer

thank you!@!!!