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If `alpha` and  `beta` are the roots of the quadratic equation x^2 – 3x -1 = 0, find...

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christiano-cr7 | (Level 1) Salutatorian

Posted September 7, 2013 at 6:00 AM via web

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If `alpha` and  `beta` are the roots of the quadratic equation x^2 – 3x -1 = 0, find the value of 1 / `alpha` + 1 / `beta`

A. –3

B. –1

C. -1/3

D. 2/3

E. 3

1 Answer | Add Yours

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 7, 2013 at 6:09 AM (Answer #1)

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`x^2-3x-1 = 0`

`alpha` and `beta` are the roots of the quadratic equation.

Then we know that;

`alpha+beta = -(-3)/1 = 3`

`alphaxxbeta = -1/1 = -1`

`1/alpha+1/beta`

`= (beta+alpha)/(alphaxxbeta)`

`= (3)/(-1)`

`= -3`

So the answer is -3 and it is in option A.

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