since the equation is quadratic AND has TWO real roots since discriminant >0 . working out through the quadratic formula, we get that the roots are 0 and 4p. Meaning the parabola px^2 - 4x + p^2 = 0 cuts the x-axis at (0,0) and (4p,0). so yes x can equal zero since the parabola passes through (0,0)