If k is one of the roots of x - 4k - 20/x = 0, how do I determine the possible values of k?​

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  no real solutions; k = ±i(2/3)√15

Step-by-step explanation:

If k is one of the roots, then substituting it for x will satisfy the equation:

  k -4k -20/k = 0

Multiplying by k gives ...

  -3k^2 -20 = 0

  k^2 = -20/3 = -6 2/3

There are no real values of k such that this is true.

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If we allow k to be imaginary, then ...

  k = ±i√(20/3) = ±i(2/3)√15

Possible imaginary values of k are ±(2/3)√15.

answer: 20

step-by-step explanation: