About quadratic form and its discriminant

Question

There are 3 parts of the problem.

1. Let d be a perfect square, possibly 0. Show that there is a quadratic form $ax^2+bxy+cy^2=0$ of discriminant d for which a=0.
   
   
2. Let a,b,c be integers with $a\ne0$. Show that if one root of the eqatuion $au^2+bu+c=0$ is rational then the other one is, and that $b^2-4ac$ is a perfect square, possibly 0.
3. Show also that if $b^2-4ac$ is a perfect square, possibly 0, then the roots of the equation $au^2+bu+c=0$ is rational.

For question 1., I wrote $d=k^2$ for some integer k. Then, I got to $b^2-k^2=4ac$ and got stuck.

For question 2 and 3, all the claims of the problem sounds perfectly right (which should be always right...) and I couldn't start from both of those ones.

Thank you.