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If D>0, the parabola cuts the x-axis at exactly two distinct points. The roots are distinct.

This case is shown in the figure,
where the quadratic polynomial cuts the x-axis at two distinct points.
If D=0, the parabola just touches the x-axis at one point and the rest of the parabola lies
above or below the x-axis. In this case, the roots are equal.

This case is shown in the figure ,
where the quadratic polynomial touches the x-axis at only a single point.

If D<0, the parabola lies entirely above or below the x-axis and there is no point of
contact with the x-axis. In this case, there are no real roots.

This case is shown in the figure ,

where the quadratic polynomial neither cuts nor touches the x-axis.

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