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$If e_{1} and e_{2} are roots of the equation x^{2} - a x + 2 = 0 where e_{1}, e_{2} are eccentricities of$
$ellipse and hyperbola respectively then range of a is$

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$(3, \infty)$

$(2, \infty)$

$(- \infty, 1) \cup (1, 2)$

$(1, \infty)$

answer is A.

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Detailed Solution

$clearly 0 < e_{1} < 1 < e_{2} both roots are positive \Rightarrow a > 0$

$\begin{array}{l} f (x) = x^{2} - a x + 2 \\ f (1) < 0 \Rightarrow 1 - a + 2 < 0 \\ 3 < a \\ \Rightarrow a > 3 \\ \Rightarrow a \in (3, \infty) \end{array}$

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