There are many answers. In all the answers c must be negative, if and only if a and b are not both zero (which would make c zero).
Let a=1 and b=2, then 14+22+c=0, 5+c=0, c=-5. This is also true for a=-1 and/or b=-2.
So you can let a and b equal any numbers and calculate c=-a4-b2.