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Math Help - Function negative for all values of x

  1. #1
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    Function negative for all values of x

    Find the range of values of m for which the function 3x^2 -12x + m is negative for all values of x.

    Is it possible for the function to be negative ? If so, how ?I tried using b^2 - 4ac < 0 and the result is m > 12 . However when i tried substituting *13* as the value of m and *1* as the value of x, the result is a positive number.
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  2. #2
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    Quote Originally Posted by Lilkaze View Post
    Find the range of values of m for which the function 3x^2 -12x + m is negative for all values of x.

    Is it possible for the function to be negative ? Mr F says: Yes, but not for all values of x.

    If so, how ?I tried using b^2 - 4ac < 0 and the result is m > 12 . However when i tried substituting *13* as the value of m and *1* as the value of x, the result is a positive number.
    Since the coefficient of x^2 is positive, it's impossible for this parabola to be negative for all values of x.
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  3. #3
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    The rules are this way :

    ax˛+bx+c

    If the discriminant is strictly negative
    The trinomial is of the same sign as a.

    If the discriminant is equal to 0
    Then it's a multiple of a perfect square and the sign is the sign of a.

    If the discriminant is positive
    There are 2 real roots x_1 and x_2
    P(x)=a(x-x_1)(x-x_2)

    And the sign of the trinomial is as following :
    - sign of a in ]-\infty ~,~x_1] \cup [x_2 ~,~+\infty[
    - inverse sign of a in [x_1 ~,~ x_2]
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