Verified answer

If r is a root of f, then (x - r) is a factor of f.

So the polynomial with roots 2 + √5 and 2 - √5 is

f = a(x - 2 - √5)(x - 2 + √5)

= a(x^2 - 2x + x√5 - 2x + 4 - 2√5 - x√5 + 2√5 - 5)

= a(x^2 - 4x - 1), where a is any nonzero real number.