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2 January, 11:45

The roots of the equation 3x²-2x-4=0 are J and K. Evaluate J² + K².

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  1. 2 January, 11:51
    0
    28/9

    Step-by-step explanation:

    If the roots are J and K, then:

    3 (x - J) (x - K) = 0

    3 (x² - (J+K) x + JK) = 0

    So if we factor out the leading coefficient:

    3x² - 2x - 4 = 0

    3 (x² - 2/3x - 4/3) = 0

    The coefficient of the second term is the sum of the roots:

    J + K = 2/3

    And the constant is the product of the roots:

    JK = - 4/3

    If we take the sum of the roots and square it:

    (J + K) ² = (2/3) ²

    J² + 2JK + K² = 4/9

    And subtract twice the product:

    J² + K² = 4/9 - 2JK

    J² + K² = 4/9 - 2 (-4/3)

    J² + K² = 4/9 + 8/3

    J² + k² = 28/9
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