If both the roots of x2 - ax + a- 0 are greater than 2 then

Let α,β be the roots such that α,β>2. aa2−4a≥0⇒a≤0 or a≥4bα+β>s=a>4cf(2)=4−a>0⇒a<4Hence, no such a exist.

If both the roots of x2 - ax + a- 0 are greater than 2 then

Let α,β be the roots such that α,β>2. aa2−4a≥0⇒a≤0 or a≥4bα+β>s=a>4cf(2)=4−a>0⇒a<4Hence, no such a exist.

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If both the roots of x² - ax + a- 0 are greater than 2 then

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$a \in (4, \infty)$

none of these

$a \in (0, 2)$

$a \in (- \infty, 4)$

answer is D.

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Detailed Solution

$Let α, β be the roots such that α, β > 2 .$
$\begin{array}{l} (a) a^{2} - 4 a \geq 0 \Rightarrow a \leq 0 or a \geq 4 \\ (b) α + β > s = a > 4 \\ (c) f (2) = 4 - a > 0 \Rightarrow a < 4 \end{array}$
Hence, no such a exist.

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If both the roots of x² - ax + a- 0 are greater than 2 then