*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.