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Parabolas and Complex Roots

How many times does the graph of a quadratic equation (a parabola) cross the x-axis?

I know that the graph of a quadratic equation should cross the x-axis 2 times, because the polynomial equation of second degree should have two roots, however if the vertex of a parabola is the orgin itself, the two points are coincident,

But what if the roots are complex? How many times would the graph cross the x-axis.

Solution Preview

Such a parabola is not possible in the real plane. If you can draw the parabola on x-y plane, it should have two real roots.

I am not quite ...

Solution Summary

Parabolas and Complex Roots are discussed.