Question 142413: Can a line have more than one x-intercept?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! That would depend on what sort of line you are talking about. If it is a straight line defined by a first-degree polynomial equation, then no. On the other hand, things like circles, ellipses, parabolas, and any other higher-order curves are lines that could possibly intersect the x-axis in more than one point.
We know that the straight line graph of a first-degree polynomial equation only intersects the x-axis in one point because of the Fundamental Theorem of Algebra. There is a direct one-to-one correspondence between the roots or zeros of an equation and the x-intercept of a graph of the equation. A root of the equation and the x-coordinate of the intercept point are identical. The Fundamental Theorem of Algebra tells us that a polynomial of degree n has exactly n roots. Therefore, a polynomial of degree 1 must have exactly 1 root, no more and no less -- hence, there is one and only one x-intercept. (note that we don't have to consider lines parallel to the x-axis because the equation of a line parallel to the x-axis is a zero degree equation)
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