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What is the simplest equation that has roots 4 and 2?

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xetaalpha | Student | (Level 2) Honors

Posted March 4, 2013 at 6:37 AM via web

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What is the simplest equation that has roots 4 and 2?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 4, 2013 at 6:43 AM (Answer #1)

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The term "simplest" in the question refers to finding an equation that only has 4 and 2 as its roots and there are no common factors in the coefficients of the terms of the equation. A quadratic equation has only 2 solutions.

If the roots are a and b, the quadratic equation is of the form x^2 - (a + b)*x + a*b = 0.

For roots 4 and 2, the simplest quadratic equation is x^2 - 6x + 8 = 0.

The required equation with roots 4 and 2 is x^2 - 6x + 8 = 0.

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gilbertbi | Middle School Teacher | (Level 1) Adjunct Educator

Posted March 4, 2013 at 7:20 PM (Answer #2)

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To find your equation, simply work the problem backwards:

Let:

x = 2       and       x = 4

x - 2 = 0   and   x - 4 = 0

(x - 2)(x - 4) = 0

From here use FOIL:

`x^2 - 6x + 8 = 0`

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