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DEEPAK SINGH PARIHAR Grade: 11
        is there anyone who can explain me the completing the square method in quadratic equation............
7 years ago

Answers : (1)

Rohith Gandhi
24 Points
										

Dear Deepak,


First recall the algebraic identities


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We shall use these identities to carry out the process called Completing the Square. For example, consider the quadratic function


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What can be added to yield a perfect square? Using the previous identities, we see that if we put 2e=8, that is e=4, it is enough to add tex2html_wrap_inline70 to generate a perfect square. Indeed we have


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It is not hard to generalize this to any quadratic function of the form tex2html_wrap_inline74 . In this case, we have 2e=b which yields e=b/2. Hence


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Example: Use Complete the Square Method to solve


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Solution.First note that the previous ideas were developed for quadratic functions with no coefficient in front of tex2html_wrap_inline84 . Therefore, let divide the equation by 2, to get


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which equivalent to


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In order to generate a perfect square we add tex2html_wrap_inline90 to both sides of the equation


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Easy algebraic calculations give


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Taking the square-roots lead to


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which give the solutions to the equation


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We have developed a step-by-step procedure for solving a quadratic equation; or, in other words, an algorithm for solving a quadratic equation. This algorithm can be stated as a formula called Quadratic Formula


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All the best Deepak !!!




Regards,

Askiitians Experts

Rohith Gandhi P

7 years ago
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