math
posted by nancy on .
Find a polynomial with integer coefficients such that (sqrt3 + sqrt5) is a root of the polynomial

Going back over some previous posts, I noticed you had posted this same question earlier, but for that you had
3 + √5 as a root.
I will answer it as if that was the right question.
If 3+√5 is a root, then its conjugate 3√5 must also be a root, or else a radical will show up in the expansion.
so the polynomial is
(x  (3+√5))(x (3√5))
= (x  3  √5)(x  3 + √5)
= x^2  3x + x√5  3x + 9  3√5  x√5 + 3√5  5
= x^2  6x + 4