Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).
x = 1 - sqrt(2)] and x = 2 + sqrt(7).
\(f(x)=(x-(1-\sqrt2))(x-(1+\sqrt2))(x-(2-\sqrt7))(x-(2+\sqrt7))\)
That should do it. You can expand. Try graphing it using desmos to check it is right first ;)
