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Math Help - x intersection

  1. #1
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    x intersection

    Determine the values of "k" if the graph y=2x^2-2x+3k intersects the x-axis at two distinct points,
    help would be cool
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  2. #2
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    Hello, bondra!

    Determine the values of k if the graph y\:=\:2x^2-2x+3k
    intersects the x-axis at two distinct points,
    In other words, the graph that parabola has two x-intercepts.

    . . That is: . 2x^2-2x + 3k \:=\:0 has two real roots.


    Quadratic Formula: . x \;=\;\frac{2 \pm \sqrt{4 - 24k}}{4}

    There are two real roots if the discriminant is positive:

    . . That is: . 4 - 24k \:>\:0 \quad\Rightarrow\quad -24k \:>\:-4 \quad\Rightarrow\quad\boxed{ k \:<\:\frac{1}{6}}

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