Roots of Quadratic Equations: Summary


First recall the quadratic formula

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The expression tex2html_wrap_inline28 that appears under the square root sign determines the nature of the roots. It is called the discriminant of the equation.

1
If tex2html_wrap_inline30 , the equation has only one root tex2html_wrap_inline32 , called double root. It is not hard to prove that in this case, we have

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2
If tex2html_wrap_inline36 , the equation has two distinct real roots tex2html_wrap_inline38 and tex2html_wrap_inline40 . In this case, we have

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If you try to prove the above equation, make use of the following identities:

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As a matter of fact, if two numbers tex2html_wrap_inline38 and tex2html_wrap_inline40 satisfy the above identities, then they are solutions to the quadratic equation tex2html_wrap_inline50 .

3
If tex2html_wrap_inline52 , the equation has two distinct complex roots that are conjugates of each other

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Mohamed Amine Khamsi
Thu Jul 11 10:08:25 MDT 1996

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