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Math Help - Discriminant

  1. #1
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    Discriminant

    Find the values of x for which 5x 2 + 3x^2 is less than zero.

    I know you have to let ∆ ≤ 0 but then im unsure how to do it??
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  2. #2
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    Quote Originally Posted by scubasteve94 View Post
    Find the values of x for which 5x 2 + 3x^2 is less than zero.

    I know you have to let ∆ ≤ 0 but then im unsure how to do it??
    for a quadratic equation
    ax^2 +bx+c = 0

    discriminant = b^2 - 4ac

    If discriminant =< 0
    Then roots are unreal

    Discriminant for your equation is 25 +(4*3*2) = 25+24 = 49

    Dont "assume the discriminant if its already given"

    ---------------------

    For your question

    5x 2 + 3x^2 < 0

    you need to find the solution set of x for which this inequality holds


    3x^2 + 5x - 2 <0

    3x^2 + 6x - x - 2 < 0

    3x(x+2) - 1(x+2) <0

    (3x-1)(x+2)<0

    (x - 1/3) (x+2) <0

    When x> 1/3
    then
    both terms are positive so this is not correct

    when -2<x <1/3
    First term is negative and 2nd is positive

    Hence its negative thus its a solution set

    similarly when x<-2
    LHS is positive thus its not a solution set

    Thus your answer is -2<x<1/3

    --------------------------------------------

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