quadratic equation

The given root is -1 +sqrt3.
Let the other root be A.
So A + (-1 +sqrt3) = -p which is rational........(1) and
A(-1+sqrt3) = q which is also rational.......(2)
From (1), for p to be rational, A must be of the form k- sqrt3. Substitute into (2),
(k- sqrt3)(-1+sqrt3) = -k - 3 + sqrt3 + ksqrt3 = q.
For q to be rational, sqrt3 + ksqrt3 = 0, therefore, k=-1.
Therefore, the other root is -1-sqrt3.

2008-07-25 22:30:49 補充：
-1-sqrt3 is called the conjugate of -1+sqrt3.

According to quadratic formula
x=[-p+√(p^2-4q)]/2
Since p andq are rational constant,and one of the roots is -1√3,whcih is irrational,so p=0,otherwise,the root may be something plus a irrational number
So √(p^2-4q)]/2=-1√3
√(-q)=-1√3
(-q)=3
q=-3
So x^2-3=0
x=√3 or x= -√3
the other root of quation is √3