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Quadratic inequalities

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data
    there are several methods to solve an quadratic inequality.
    1:by graph
    2:if (x-a)(x-b) > 0,(x-a) > 0 and (x-b) > 0 or (x-a) < 0 and (x-b) < 0.......
    3.Using test value method
    i.e.Find a and b in the expanded form of (x-a)(x-b)
    a and b are the critical values,then we take a value of x from different interval and check whether it satisfies the
    inequality or not.

    2. Relevant equations

    3. The attempt at a solution
    We need to factorize before using method 2 and 3.
    Is there any method to solve an quadratic inequality without factorizing?
    Last edited: Oct 7, 2012
  2. jcsd
  3. Oct 7, 2012 #2


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    By factoring the quadratic into (x-a)(x-b) you are essentially solving a quadratic equation.

    Rather than doing the factoring, use the quadratic formula to find the two roots, a and b. The answer will be the same as if you factored the quadratic, provided that certain basic conditions are met.
  4. Oct 9, 2012 #3
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