It is common that we need to know how many solutions a quadratic equation may have. However, we don’t necessarily need to go through the hassle of using the Quadratic Formula to figure out what the solutions actually are. The Discriminant is out solution.
The Discriminant enters stage-left. This character plays an important role. Using the discriminant we can easily gather some important information about the solutions (or zeros) of a quadratic equation.
Starting from the equation of a quadratic in standard from; ax2+bx+c = 0, the discriminant is b2 – 4ac. Because this is the argument to a square root operation, we can make some inferences.
- If b2 – 4ac > 0. i.e. the discriminant is a positive number, then the quadratic will have two real solutions. The graph will cross the x-axis in two locations.
- If b2 – 4ac = 0. Then the quadratic will have exactly one solution. The graph will bounce off the x-axis in one location.
- If b2 – 4ac < 0. i.e. the discriminant is a negative number, then the quadratic will have no real solutions. The graph will not touch the x-axis at any point.
Learn how to derive the quadratic formula here.
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