Question

Compare and contrast the solutions of ax^2 + h = 0 to the solutions of ax^2 = h, where a and h are positive.

Answer 1

well, you have

ax^2 = -h
ax^2 = h

In either case, a and h must have the same sign, since x^2 is always positive.

Unless x=0, in which case, h=0.

x = ±√|h/a|

Naturally, if a=0, there is no solution unless h is also zero.