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3 December, 13:23

Find the value of k for which one root of the quadratic equation kx2 14x 8 = 0 is 6 times the other

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  1. 3 December, 13:47
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    k = 3.

    Step-by-step explanation:

    If the 2 roots are A and B we have the relations:

    AB = 8/k and A+B = - 14/k.

    We are given that A = 6B so

    6B^2 = 8/k

    B^2 = 8/6k = 4/3k

    B = 2 / √ (3k) ... (1)

    Now A + B = - 14/k so

    6B + B = 7B = - 14/k

    B = - 2/k ... (2)

    Eliminating B from equations (1) and (2):

    2 / √ (3k) = - 2/k

    Cross multiply:

    2k = - 2√ (3k)

    Squaring both sides:

    4k^2 = 4 * 3k

    4k^2 = 12k

    k^2 = 3k

    k = 3.
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