1. ## 2 polynomial problems

problem 1
let f(x) and g(x) be two quadratic polynomials all of whose coefficients are rational numbers.suppose f(x) and g(x) have a common irrational root.show that g(x)=r.f(x),for some rational number r.

problem 2
suppose the roots of x^2+px+q = 0 are rational numbers and p and q are integers.
then show that the roots are integers.

2. How far have you progressed ?

3. Originally Posted by earthboy
problem 1
let f(x) and g(x) be two quadratic polynomials all of whose coefficients are rational numbers.suppose f(x) and g(x) have a common irrational root.show that g(x)=r.f(x),for some rational number r.
For such a polynomial the irrational roots occur in conjugate pairs, if such quadratics share one irrational root they have identical roots.

CB

4. Originally Posted by earthboy;563081[B
problem 2
[/B]suppose the roots of x^2+px+q = 0 are rational numbers and p and q are integers.
then show that the roots are integers.
Because this is a monic polynomial the rational roots theorem gives the required result immediately

CB