1. The problem statement, all variables and given/known data A charge of +2q is placed at the origin and a second charge of -q is placed a x = 3cm. Where can a third charge +Q be placed so that it experiences a zero force? 2. Relevant equations F=kQ1Q2/r^2 3. The attempt at a solution OK I thought I had this until the roots of the quadratic I am solving come out to be imaginary... Q1 = 2q Q2 = -q Q3 = +Q I am assuming that Q3 must be placed to the right of Q2. the distance between Q1 and Q3 = x+0.03m and the distance between Q2 and Q3 = x If F on Q3 = 0 then FQ1=FQ2 at this point F1on3 = k*Q1*Q3/r^2 = F 2on3 = k*Q2*Q3/r^2 ;; cancel k and Q3 Q1/r1to32 = Q2/r2to32 Q1/(x+0.03m)2=Q3/x2 Q1*x2 = Q3*(x+0.03m)2 2q*x2 / -q = (x+0.03m)2 -2x2 = (x+0.03m)2 -2x2 = x2 + 0.06x + 0.0009 0=3x2 + 0.06x + 0.0009 Can anyone tell me where I've gone wrong here? Is my assumption that Q3 is to the right of Q2 incorrect?