If $(\alpha + \sqrt {\beta})$ and $(\alpha - \sqrt {\beta})$ are the roots of the equation $x^{2} + px + q = 0$, where $\alpha, \beta, p$ and $q$ are real, then the roots of the equation $(p^{2} - 4q) (p^{2} x^{2} + 4px) - 16q = 0$ are
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$\left (\dfrac {1}{\alpha} + \dfrac {1}{\sqrt {\beta}}\right )$ and $\left (\dfrac {1}{\alpha} - \dfrac {1}{\sqrt {\beta}}\right )$
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$\left (\dfrac {1}{\sqrt {\alpha}} + \dfrac {1}{\beta}\right )$ and $\left (\dfrac {1}{\sqrt {\alpha}} - \dfrac {1}{\beta}\right )$
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$\left (\dfrac {1}{\sqrt {\alpha}} + \dfrac {1}{\sqrt {\beta}}\right )$ and $\left (\dfrac {1}{\sqrt {\alpha}} - \dfrac {1}{\sqrt {\beta}}\right )$
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$(\sqrt {\alpha} + \sqrt {\beta})$ and $(\sqrt {\alpha} - \sqrt {\beta})$
A
Correct answer
Explanation
The roots of x^2 + px + q = 0 are alpha +/- sqrt(beta). Thus, sum of roots = -p = 2*alpha and product = q = alpha^2 - beta. Substituting these into the second equation and solving for x reveals the roots are 1/(alpha +/- sqrt(beta)).