Hi there... I need help on this question

If you are sketching the graph of a quadratic function and the graph only touches the x-axis at one point, then the discriminant is:

A.a rational number
B.a positive number
C.zero
D.a negative number
E.an irrational number

Here is an entry on wikipedia about discriminants: Discriminant - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Discriminant)

In this, it is stated that:

When D = 0, P(x) has two coincident real roots x_1=x_2=-\frac{b}{2a}. And its graph is tangent to the x-axis.
I believe this answers your question.

Agreed. A quadratic function always has two roots. They can be real or complex. If you're looking at a graph, the real roots are where the graph crosses the x-axis. If the graph never crosses the x-axis, both the roots are complex. If the graph is tangent to the x-axis, then it only touches at one point, and has two identical real roots.

If you think of it in terms of the quadratic equation, the discriminant is the thing that separates the two roots because of the +/- sign. So the only way to make the two roots identical is by having the discriminant be zero, so that adding it and subtracting it give the same result.