Question 868265: Write. Polynomial function with rational coefficient in standard form with the given zeros x=3+i,2-i Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! If a polynomial with rational coefficients has a non-real zero, it must also have the conjugate non-real zero.
That is to say that if is a zero, must be a zero too.
That means that the factorization of the polynomial must contain the factors and .
So the polynomial must have as a factor .
The same applied to the zero means that and area factors,
and the polynomial must have as a factor .
In sum, the polynomial must have for a factor .
The simplest answer would be .
Of course, multiplying that polynomial by any rational number we can get another answer,
like ,
or .
