Roots of Quadratic Equations: Summary
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.
- If , the equation has only one root , called double root. It is not hard to prove that in this case, we have
- 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 .
- If , the equation has two distinct complex roots that are conjugates of each other
Mohamed Amine Khamsi
Thu Jul 11 10:08:25 MDT 1996
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