Find the possible values of c such that the line with equation y = 2x + c twice intersects the parabola with equation y = x^2 + 3x

Question

Find the possible values of c such that the line with equation y = 2x + c twice intersects the parabola with equation y = x^2 + 3x

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2 weeks 2021-10-06T06:51:16+00:00 2 Answers 0

Answers ( )

  1. Ava
    0
    2021-10-06T06:52:21+00:00

    Answer:

    c > -¼

    Step-by-step explanation:

    x² + 3x = 2x + c

    x² + x – c = 0

    Since they intersect at 2 points,

    B²-4AC > 0

    (1)²-4(1)(-c) > 0

    1 + 4c > 0

    c > -¼

  2. Ava
    0
    2021-10-06T06:52:56+00:00

    Answer:

    C>-1/4

    Step-by-step explanation:

    Two have intersection it must be:

    2x+c= x^2+3x, i.e,

    x^2+x-c=0

    Solution of its equation is:

     x_{1,2}=\frac{-1+-\sqrt{1^2+4c}}{4c}

    If we we want two solution we must have that:

    1+4c>0

    So c>-1/4.

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