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Math Help - [SOLVED] polynomial inequality

  1. #1
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    [SOLVED] polynomial inequality

    Can someone assist me with this? I'm supposed to find the range of valid answers

    x^2+2x-3 < 0

    typically I'd just factor the left to figure out the zeros to get my critical points, then check each area to find the valid ranges. However, I can't factor the equation...unless I'm mistaken, it's not factorable. How do I get the answer?
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  2. #2
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    (x+3)(x-1)
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  3. #3
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    Quote Originally Posted by satis View Post
    Can someone assist me with this? I'm supposed to find the range of valid answers

    x^2+2x-3 < 0

    typically I'd just factor the left to figure out the zeros to get my critical points, then check each area to find the valid ranges. However, I can't factor the equation...unless I'm mistaken, it's not factorable. How do I get the answer?
    x^2+2x-3=(x+3)(x-1)

    In order for this to be < 0,
    one factor must be positive and the other negative.

    Hence, if x+3 is positive, x > -3.
    x-1 remains negative until x=1.
    Hence -3 < x < 1

    Also if x+3 is negative, x < -3
    There is no way this range of x allows x-1 to be positive however.

    Therefore -3 < x < 1.

    Or, the graph is a parabola with the minimum under the x axis.
    Hence, it's negative between the roots.
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