Let f(x) = ax2 + bx + c
If f(x) has two real and distinct zeroes, the parabola represented by f(x) cuts x-axis at two distinct points.
If f(x) has two real and equal zeroes, the parabola represented by f(x) touches x-axis at only one distinct point.
Hence, if the parabola represented by f(x) = ax2 + bx + c cuts x-axis at two distinct points, then the polynomial ax2 + bx + c has 2 real zeroes.