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.

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

problem 2

then show that the roots are integers.

please help!and please give the problem number to your answers