If a and $\beta$ are the roots of the equation $ax^2+2bx+c=0$, then $\sqrt {a/\beta}+\sqrt {\beta /a}$ is equal to

Using the quadratic formula, the roots of the equation are evaluated as a = (-2b + sqrt(4b^2 - 4ac))/(2a) and beta = (-2b - sqrt(4b^2 - 4ac))/(2a). The required expression is sqrt(a/beta) + sqrt(beta/a), which combines to (a + beta)/sqrt(a*beta). Using Vieta's formulas for sum and product of roots, a + beta = -2b/a and a*beta = c/a. Substituting these values gives (-2b/a) / sqrt(c/a), which simplifies to -2b / sqrt(ac). The result is -2b/sqrt(ac).

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