The values of for which each one of the roots of $x^{2} - 4 a x + 2 a^{2} - 3 a + 5 = 0$ is greater than $2$ , are

a \in (1, \infty)

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a = 1

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a \in (\infty, 1)

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a \in (9 / 2, \infty)

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Solution

The correct option is A $a \in (1, \infty)$
Let $(α, β)$ be root of equation $x^{2} - 4 a x + 2 a^{2} - 3 a + 5 = 0 . . . (1)$
Given $α > 2$ & $β > 2$
now $α + β > 4... (2)$
From eq (1) $α + β = 4 a$ & $α β = 2 a^{2} - 3 a + 5$
using eq(2) $4 a > 4$
$a > 1$
Hence $a ϵ (1, \infty)$

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