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The set of values of ‘b’ for which the origin and the point (1,1) lie on the same side of the straight line $a^{2} x + a b y + 1 = 0, \forall a \in R, b > 0$ are

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$b \in (2, 4)$

$b \in (0, 2)$

$b \in [0, 2]$

$b \in [0, 3]$

answer is B.

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Detailed Solution

$D < 0 \Rightarrow b^{2} - 4 < 0 \Rightarrow - 2 < b < 2$ but b > 0

$∴$ $0 < b < 2$ ie., $b \in (0, 2)$

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