I could use some help with this:
Find a polynomial of degree three with real number coefficients and zeros of 3 + i and -7.
Kind of having trouble with the real number coefficients, and how to find them?
(x+7)
(x - (3+1))
(x + (3-1))
Is that how you write 3 + i as a zero?
Any help is greatly appreciated! Thanks!
For to be a root, then is a factor.
For to be a root, then is a factor.
Since complex solutions always appear as complex conjugates, that means is also a solution. So is another factor.
So your polynomial is of the form
Expanding gives
This equation will hold true for any value of a.
For simplicity, let and then you have your cubic.