Geometric meaning of zeros of a polynomial :
The zeroes of a polynomial p(x) are the x-coordinates of the points where the graph of y=p(x) intersects the x-axis
For any quadratic polynomial ax2 + bx + c, 'a' not equal to 0 the graph of the corresponding equation y = ax2 + bx + c has one of the two shapes either open upwards like U or open downwards depending on whether a > 0 or a < 0. (These curves are called parabolas)
This fact is true for any quadratic polynomial i.e. the zeroes of a quadratic polynomial ax2 + bx + x, a not equal to 0 are precisely the parabola representing y = ax2 + bx + c intersects the x - axis.