Question

Where can we apply D=0 and D>0 and D<0 in the problems of parabola and why we apply this

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Answer 1

A quadratic equation is really a equation of parabola.

Case 1:
D = 0,
Tip of Parabola is just touching x-axis (vertex) . ie; only one point is touching.

Case 2:
D > 0,
Parabola is touching on x-axis at two points. ie; parabola is cut by x axis.

Case 3:
D < 0
Parabola is not touching x-axis.

Here the points on x- axis is the root.