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How to find m in x^-5x+m=0 x1=2x2 (this is not 2 times 2) using vieta's formulas?

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lexiebravo | Student, Grade 10 | eNotes Newbie

Posted December 3, 2011 at 9:51 PM via web

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How to find m in x^-5x+m=0 x1=2x2 (this is not 2 times 2) using vieta's formulas?

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lexiebravo | Student, Grade 10 | eNotes Newbie

Posted December 4, 2011 at 1:11 AM (Answer #1)

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Thank you.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 3, 2011 at 11:41 PM (Answer #2)

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Apply Vieta's formulas to a quadratic equation `ax^2 + bx + c = 0` :

`x_1 + x_2 = -b/a`

`` `x_1*x_2 = c/a`

Compare the standard quadratic equation with your equation and find coefficients a = 1, b=-5 and c=m.

Write Vieta's formulas:

`x_1 + x_2 = 5`

`` `x_1*x_2 = m`

Use the relation between roots:`x_1 = 2x_2`

`x_1 + x_2`  = 5 <=> `2x_2 + x_2 ` = `3x_2 = 5`  => `x_2 = 5/3`  => `x_1 = 10/3`

`x_1*x_2 ` = m => `(10/3)*(5/3)`  = m => m = `50/9`

The value of m is m = `50/9` .

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