preap Algebra 2
posted by Sam on .
write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: 2,2,1,3, sqrt 11

(x+2)(x2)(x+1)(x3) takes care of the integer roots.
Now, if √11 is a root, then (x√11) is a factor, but that leaves a dangling √11, which will show up in the coefficients. So, you also need to include (x+√11), since
(x√11)(x+√11) = x^2121, which has rational coefficients.
So, the final polynomial is
f(x) = (x+2)(x2)(x+1)(x3)(x√11)(x+√11)
and yu can expand that out if you like. 
oops. (x√11)(x+√11) = x^211