use the discrminant to determine all values of k which would result in the equation -3x^2-6x+k=0 having real,unequal roots.​ must be right t

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use the discrminant to determine all values of k which would result in the equation -3x^2-6x+k=0 having real,unequal roots.​ must be right ty helppp asap

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Hưng Khoa 1 year 2021-08-18T17:31:44+00:00 1 Answers 0 views 0

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    2021-08-18T17:33:05+00:00

    Answer:

    [tex]k>-3[/tex]

    Step-by-step explanation:

    We have the equation:

    [tex]-3x^2-6x+k=0[/tex]

    Where a = -3, b = -6, and c = k.

    And we want to determine values of k such that the equation will have real, unequal roots.

    In order for a quadratic equation to have real, unequal roots, the discriminant must be a real number greater than 0. Therefore:

    [tex]b^2-4ac>0[/tex]

    Substitute:

    [tex](-6)^2-4(-3)(k)>0[/tex]

    Simplify:

    [tex]36+12k>0[/tex]

    Solve for k:

    [tex]12k > -36[/tex]

    [tex]k>-3[/tex]

    So, for all k greater than -3, our quadratic equation will have two real, unequal roots.

    Notes:

    If k is equal to -3, then we have two equal roots.

    And if k is less than -3, then we have two complex roots.

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