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31 August, 15:43

Find the discriminant of the quadratic $3x^2 - 7x + 6.$

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  1. 31 August, 15:46
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    Solve for x:

    3 x^2 - 7 x + 6 = 0

    Divide both sides by 3:

    x^2 - (7 x) / 3 + 2 = 0

    Subtract 2 from both sides:

    x^2 - (7 x) / 3 = - 2

    Add 49/36 to both sides:

    x^2 - (7 x) / 3 + 49/36 = - 23/36

    Write the left hand side as a square:

    (x - 7/6) ^2 = - 23/36

    Take the square root of both sides:

    x - 7/6 = (i sqrt (23)) / 6 or x - 7/6 = - (i sqrt (23)) / 6

    Add 7/6 to both sides:

    x = 7/6 + (i sqrt (23)) / 6 or x - 7/6 = - (i sqrt (23)) / 6

    Add 7/6 to both sides:

    Answer: x = 7/6 + (i sqrt (23)) / 6 or x = 7/6 - (i sqrt (23)) / 6
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