If $a, b$ are the roots of the equation $(p^{2} + p + 1) x^{2} + (p - 1) x + p^{2} = 0$ such that unity lies between the roots then the set of values of $p$ is

ϕ

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p ϵ (- 1, 0)

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p ϵ (- 1, 1)

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none of these

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Solution

The correct option is B $p ϵ (- 1, 0)$
$f (x) = (p^{2} + p + 1) x^{2} + (p - 1) x + p^{2} = 0 u n i t y l i e s b e t w e e n t h e r o o t s ∴ f (1) < 0 f (1) = (p^{2} + p + 1) + (p - 1) + p^{2} < 0 2 p^{2} + 2 p < 0 p^{2} + p < 0 p (p + 1) < 0 ∴ p \in (- 1, 0)$

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