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If $p x^{2} + q x + r = 0$ is a quadratic equation $(p, q, r \in R)$ such that its roots are $α, β$ and $p + q + r < 0, p - q + r < 0$ and $r > 0,$ then $[α] + [β] = - - - -$ Where $[.]$ denotes greatest integer function

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Detailed Solution

Given equation is $p x^{2} + q x + r = 0$

Let, $f (x) = p x^{2} + q x + r$

$f (0) = r > 0$

$f (1) = p + q + r < 0$

$f (- 1) = p - q + r < 0$

Hence, one root lies in $(- 1, 0)$ and the other in $(0, 1)$

$∴ [α] = - 1$ and $[β] = 0 \Rightarrow [α] + [β] = - 1$

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