p is a nonzero real root of the equation: ax^{2}+ bx + c = 0 and, q is a nonzero real root of the equation: -ax^{2}+ bx + c = 0.
Does the equation ax^{2}/2 + bx + c = 0 always have a root between p and q?
If so, prove it. Otherwise, give a counter example.
Note: Each of a, b and c is a nonzero real number.