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4 June, 00:07

Find the roots of the parabola given by the following equation.

2x2 + 5x - 9 = 2x

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Answers (1)
  1. 4 June, 00:11
    0
    x=-3 or x=3/2

    Step-by-step explanation:

    We are given the following equation:

    2x^2+5x-9=2x

    We are asked to find the roots. That means just solve it for x.

    2x^2+5x-9=2x

    Subtract 2x on both sides:

    2x^2+3x-9=0

    Let's see if we can put this in factored form.

    Compare

    2x^2+3x-9=0

    and

    ax^2+bx+c=0.

    a=2, b=3, c=-9

    We have to find two numbers that multiply to be ac and add up to be b.

    ac=-18

    b=3

    What are two numbers that multiply to be - 18 and add to be 3?

    Say - 3 and 6.

    So we are going to factor 2x^2-3x+6x-9=0

    The first two terms have a common factor of x.

    The last two terms have a common factor of 3.

    2x^2-3x+6x-9=0

    x (2x-3) + 3 (2x-3) = 0

    Now we can factor the (x-3) out of those 2 terms there since they share that common factor:

    (x+3) (2x-3) = 0

    (x+3) (2x-3) = 0 implies x+3=0 or 2x-3=0.

    So we must solve x+3=0 and 2x-3=0

    x+3=0

    Subtract 3 on both sides:

    x=-3

    2x-3=0

    Add 3 on both sides:

    2x=3

    Divide both sides by 2:

    x=3/2

    The solutions are x=3 or x=-3/2
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