The Discriminant

When an equation is in the standard quadratic form we can identify parts of the equation. The first “part” we will identify is called the “Discriminant”. The discriminant is a value which characterizes certain properties of a quantity’s roots. Using the standard quadratic form the discriminant is defined by

If we would examine several different quadratics and their graphs we would eventually determine that:

• If the discriminant is 0 the curve will cross the x-axis only once. The solution will be one real root
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• If the discriminant is >0 the curve will cross the x-axis twice. The solution will be two real roots
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• If the discriminant is < 0 the curve will not cross the x-axis. The solution will be no real roots
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