Net force is Zero, quadratic answers

[flyingpig]

Homework Statement

Three point charges lie along the x axis. The positive charge q1 = 15.0uC and is at x = 2.00m (2.00 away from the origin), the positive q2 = 6.00uC is at the origin. The net force on q3 which is between q2 and q1 is 0. What is the x coordinate of q3?


solution

My book (serway and jewett, 8ed, pg 665) says x = 0.775 from 3x^2 + 8x - 8 = 0

the other x = -3.44m

The book says the negative one is (and here I quote) "the magnitude of the forces on q3 are equal, but both forces are in the same direction".


Unfortunately I have no idea what that means, based on my knowledge, isn't the negative one just another point where it satisfies the conditon? So if it was moved to satisfy x = -3.44, then x = 0.755 would be rejected?

 

[Pengwuino]

If every charge is positive, would it make sense that the third positive charge could lie on the left-hand side of the first two charges and not feel a force?

The -3.44m is an unphysical answer. It is kind of like the typical ball falling off of a cliff kinematic problem where if you were asked to calculate the time the ball hits the ground, you'll find 2 times due to the quadratic nature of the calculation. One relates to the real situation where the ball hits the ground on the right hand side and the other one is as if time were reversed and the ball went from the top of the hill to the ground in the opposite direction (though the hill is in the way...). I hope that makes sense...