Question

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

Answer 1

(x+2)(x-2)(x+1)(x-3) 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^2-121, which has rational coefficients.

So, the final polynomial is

f(x) = (x+2)(x-2)(x+1)(x-3)(x-√11)(x+√11)

and yu can expand that out if you like.

Answer 2

oops. (x-√11)(x+√11) = x^2-11