SOLUTION: Write. Polynomial function with rational coefficient in standard form with the given zeros x=3+i,2-i

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 .
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