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What is the general method to construct a quadratic equation given the roots.

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carolinesmiths | Student, Kindergarten | Salutatorian

Posted March 10, 2013 at 5:41 AM via web

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What is the general method to construct a quadratic equation given the roots.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 10, 2013 at 5:45 AM (Answer #1)

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A quadratic equation has two roots. Take the roots of the equation that has to be constructed as `x_1` and `x_2` . The quadratic equation is `(x - x_1)(x - x_2) = 0`

=> `x^2 - x_1*x + x_2*x + x_1*x_2 = 0`

=> `x^2 - (x_1 + x_2)*x + x_1*x_2 = 0`

The general form of a quadratic equation with roots `x_1` and `x_2` is `x^2 - (x_1 + x_2)*x + x_1*x_2 = 0`

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