Find a monic quartic polynomial with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).
x = 1 + sqrt 2 and 2 - sqrt 7 are also roots
We have
(x - ( 1 + sqrt 2) ) ( x - (1 - sqrt 2) ) ( x - ( 2 + sqrt 7)) ( x - (2 - sqrt 7))
Expanding this we get
x^4 - 6 x^3 + 4 x^2 + 10 x + 3
