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Solve the quadratic inequality : x^2 - 5x + 6 <= 0

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asicannot | Student, Kindergarten | eNoter

Posted July 6, 2013 at 5:31 AM via web

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Solve the quadratic inequality : x^2 - 5x + 6 <= 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 6, 2013 at 5:36 AM (Answer #1)

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The inequality x^2 - 5x + 6 `<=` 0 has to be solved.

x^2 - 5x + 6 `<=` 0

=> x^2 - 3x - 2x + 6 `<=` 0

=> x(x - 3) - 2(x - 3) `<=` 0

=> (x - 2)(x - 3) `<=` 0

This is true in two case:

  • x - 2 `<=` 0 and x - 3 `>=` 0

=> x `<=` 2 and x `>=` 3

This is not possible.

  • x - 2 `>=` 0 and x - 3 `<=` 0

=> x `>=` 2 and x `<=` 3

This is true for x lying in [2, 3]

The solution of the inequality is [2, 3]

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