SOLUTION: Find a polynomial function of least degree having only one real coefficients, a leading coefficient of 1, and roots 1-square root 3 , 1+square root 3, and 6-i .

Question 1023290: Find a polynomial function of least degree having only one real coefficients, a leading coefficient of 1, and roots 1-square root 3 , 1+square root 3, and 6-i .
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The roots we know of are the real roots
, and ,
and the complex root .
For the polynomial to have only real coefficients,
it must also have the conjugate complex root .
So, the polynomial of least degree, with a leading coefficient of is
.

From here on, it is just busywork.
That is the part where I get bored and distracted, and make mistakes, so check my math from this point on.

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