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$I f a, b, c a r e r e a l i f a x^{2} + b x + c = 0 h a s t w o r e a l r o o t s α, β w h e r e α < - 1; β > 1 t h e n$

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a

$1 - \frac{c}{a} + | \frac{b}{a} | < 0$

b

$c = 0$

c

$\frac{c}{a} + | \frac{b}{a} | - 1 > 0$

d

$1 + \frac{c}{a} + | \frac{b}{a} | < 0$

answer is A.

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Detailed Solution

$\begin{array}{l} G i v e n E q u a t i o n a x^{2} + b x + c = 0 \\ G i v e n α < - 1, β > 1 t h e n \\ f (- 1) f (1) < 0 \\ \Rightarrow (a + b + c) (a - b + c) < 0 \\ \Rightarrow (\frac{c}{a} + \frac{b}{a} + 1) (\frac{c}{a} - \frac{b}{a} + 1) < 0 \\ \Rightarrow \frac{c}{a} + | \frac{b}{a} | + 1 < 0 \end{array}$

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