Under what circumstances can the third particle be placed

Question

Suppose that in Figure, |q₂| > |q₁| > 0 but these partides may carry charges of the same or opposite type. A third particle carrying charge q₃ is to be placed in this system along the axis such that the vector sum of electric forces on the third particle is zero.

In which region I, II, or III might this be possible if

(a) q₁ and q₂ have the same sign and

(b) q₁ and q₂ have opposite signs?

(c) Under what circumstances can the third particle be placed in region I and have the vector sum of electric forces exerted on it be zero?