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29 March, 17:52

The quadratic polynomial x^2 + mx+n has roots twice those of x^2 + px+m, and none of m, n, and p is zero. What is the value of n/p?

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  1. 29 March, 21:14
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    n/p = 8.

    Step-by-step explanation:

    If the roots of the first equation are A and B we have

    A + B = - m and AB = n.

    This has roots twice the roots of the second equation so we have:

    0.5 (A + B) = - p and 0.25AB = m.

    So A + B = - 2p and AB = 4m

    Equating values of A + B and AB:

    -m = - 2p and n = 4m

    m = 2p and m = n/4

    2p = n/4

    n = 8p

    n/p = 8.
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