Posted by **nancy** on Saturday, March 6, 2010 at 10:43pm.

Find a polynomial with integer coefficients such that (sqrt3 + sqrt5) is a root of the polynomial

- math -
**Reiny**, Saturday, March 6, 2010 at 11:50pm
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

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