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What are integers roots of inequality `x^2+x-6<=0` ?

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greenbel | Honors

Posted June 30, 2013 at 5:16 PM via web

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What are integers roots of inequality `x^2+x-6<=0` ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 30, 2013 at 5:38 PM (Answer #2)

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You need to attach the equation `x^2 + x - 6 = 0` and you may use quadratic formula to evaluate its solutions, such that:

`x_(1,2) = (-1+-sqrt(1 + 24))/2`

`x_(1,2) = (-1+-5)/2 => x_1 = 2; x_2 = -3`

You should notice that the inequality holds for `x in [-3,2]` .

The problem only requests the integer solutions that satisfy the inequality `x^2 + x - 6 <= 0` , hence, you need to solve the following basic set operation, such that:

`x in [-3,2] nn Z => x in {-3,-2, -1,0, 1, 2}`

Hence, evaluating the integer solutions to the given inequality yields `x in {-3,-2, -1,0, 1, 2}` .

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