Question 176936: I am searching for a polynomial function of 'f' of least degree that has rational cooeficients, a leading coefficient of 1, and the given zeros.
3i, 2 - i
Your assistance will be greatly appreciated.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a polynomial function of 'f' of least degree that has rational cooeficients, a leading coefficient of 1, and the given zeros.
3i, 2 - i
----------------------------
To have rational coefficients -3i and 2+i must also be zeros.
--------------------------
f(x) = (x-3i)(x+3i)(x-(2-i))(x-(2+i))
f(x) = (x^2+9)((x-2)+i)((x-2)-i)
f(x) = (x^2+9)((x-2)^2 + 1)
f(x) = (x^2+9)(x^2-2x+5)
I'll leave the rest to you.
The degreewill be "4" when you are finished.
====================================
Cheers,
Stan H.
|
|
|
