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  • Digg it UP - A B C of Solving Quadratic Equation

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    ic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an

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    An expression of the type a x ? + b x + c = 0 , ( a ≠ 0 ) is called a quadratic equation in the variable x .

    The equation a x ? + b x + c = 0 is called the general (or, standard form) We can solve a quadratic equation by (1) factorization or by (2) applying the formula.

    The formula of finding the roots of the quadratic equation is as follows

    x = (- b ± √ (b ? - 4 a c) ) / 2 a

    Now we will discuss how to solve applied problems. Due to wide variety of applied problems, there is no single solving technique that works in all cases. However the following suggestion proved helpful.

    Step: 1 Read the problem carefully and determine what quantity (s) must be found.

    Step: 2 assign a variable name to the quantity.

    Step: 3 try expressing the problem algebraically, and as well determining which expressions are equal and write the necessary equation (s).

    Step: 3 solve the resulting equation (s)

    Now go through a simple problem based on formation of quadratic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an e

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    r by (2) applying the formula.

    The formula of finding the roots of the quadratic equation is as follows

    x = (- b ± √ (b ? - 4 a c) ) / 2 a

    Now we will discuss how to solve applied problems. Due to wide variety of applied problems, there is no single solving technique that works in all cases. However the following suggestion proved helpful.

    Step: 1 Read the problem carefully and determine what quantity (s) must be found.

    Step: 2 assign a variable name to the quantity.

    Step: 3 try expressing the problem algebraically, and as well determining which expressions are equal and write the necessary equation (s).

    Step: 3 solve the resulting equation (s)

    Now go through a simple problem based on formation of quadratic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an

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    s, there is no single solving technique that works in all cases. However the following suggestion proved helpful.

    Step: 1 Read the problem carefully and determine what quantity (s) must be found.

    Step: 2 assign a variable name to the quantity.

    Step: 3 try expressing the problem algebraically, and as well determining which expressions are equal and write the necessary equation (s).

    Step: 3 solve the resulting equation (s)

    Now go through a simple problem based on formation of quadratic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an

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    Step: 3 try expressing the problem algebraically, and as well determining which expressions are equal and write the necessary equation (s).

    Step: 3 solve the resulting equation (s)

    Now go through a simple problem based on formation of quadratic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an

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    ic equation and solving

    Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21 . Find the fraction.

    Solution:

    Let the numerator of the fraction be x (x be an element of I ) Then its denominator is (2x + 1).

    So the fraction is x / (2x + 1))

    And the reciprocal would be (2 x + 1) / x

    According to the problem:

    (X / (2 xs + 1)) + ((2 x + 1) / x) = ( 58 / 21 )

    (X ? + (2 x + 1) ?) / (x + (2x + 1)) = ( 58 / 21)

    [L. C. D is = ( x + ( 2x + 1 ) ]

    21 ( x ? + 4 x ? + 4 x + 1 ) = 58 x ( 2x + 1 )

    105 x? + 84 x + 21 = 116 x ? + 58 x

    11 x ? - 26 x - 21 = 0

    11 x ? - (33 - 7) x - 21 = 0 [using middle term factorization]

    11 x ?- 33 x + 7 x - 21 = 0

    11 x ( x - 3 ) + 7 ( x - 3 ) = 0

    (x – 3) (11 x + 7) = 0

    Either ( x - 3 ) = 0 , or ( 11x + 7 ) = 0 [ using zero factor theorem ]

    x = 3 ,

    From, (11x + 7) = 0

    We get, x = - (7 / 11)

    But x is an integer , neglect x = - (7

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