If $8x^2 - 2kx + k = 0$ is a quadratic equation in $x$, such that one of its roots is $p$ times the other, and $p, k$ are positive real numbers, then $k$ equals

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C - $2(\sqrt{p} + \frac{1}{\sqrt{p}})^2$. Roots r and pr: r(1+p) = k/4 and p r^2 = k/8. Eliminating r: k^2/16 = k(1+p)^2/(8p), so k = 2(1+p)^2/p = 2(sqrt(p)+1/sqrt(p))^2.

Answer

A - $(p + \frac{1}{p})$

Answer

B - $2(p + \frac{1}{p})$

Answer

D - $(\sqrt{p} + \frac{1}{\sqrt{p}})^2$

If \(8x^2 - 2kx + k = 0\) is a quadratic equation in \(x\), such that one of its roots is \(p\) times the other, and \(p, k\) are positive real numbers, then \(k\) equals

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