First recall the quadratic formula

The expression that appears under the square root sign determines the nature of the roots. It is called the **discriminant** of the equation.

**1**- If , the equation has only one root , called double root. It is not hard to prove that in this case, we have
**2**- If , the equation has two distinct real roots and . In this case, we have
If you try to prove the above equation, make use of the following identities:

As a matter of fact, if two numbers and satisfy the above identities, then they are solutions to the quadratic equation .

**3**- If , the equation has two distinct complex roots that are conjugates of each other

Thu Jul 11 10:08:25 MDT 1996

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