Find a monic quartic polynomial with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).
+23246 Since one of the roots is 1 - sqrt(2), another root will be 1 + sqrt(2).
Since one of the roots is 2 + sqrt(7), another root will be 2 - sqrt(7).
One possible solution is: ( x - [1 - sqrt(2)] ) · ( x - [1 + sqrt(2)] ) · ( x - [ 2 + sqrt(7) ] ) · ( x - [ 2 - sqrt(7) ] ) = 0
Other solutions can be found by multiplying that solution by an non-zero real number.
