Two inequality questions (not related)

1. if k does not equal 0 solve the quadratic inequation for all real values

k^2x+kx+2k<0

2. Consider the quadratic equation ax^2+px+aq+q=0 where, a does not equal 0 & p and q are constants.

It is known that one of the roots of the quadratic equation is always 1 regardless of the value of a. Prove that p+q=0