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Quadratic Equations

If α β ...

Question

If $α$ & $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0,$ where $c < 0 < b$ , then

A

0 < α < β

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B

α < 0 < β < | α |

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C

α < β < 0

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D

α < 0 < | α | < β

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Solution

The correct option is B $α < 0 < β < | α |$
$α + β = (\frac{- b}{1}) = - v e h e n c e e i t h e r b o t h r o o t s a r e n e g a t i v e o r o n e i s - v e a n d m a g n i t u d e g r e a t e r t h a n$
$t h e + v e r o o t . n o w$
$α + β = (\frac{c}{1}) = - v e$
Hence it is confirmed that one
$r o o t i s - v e a n d o t h e r a r e i s + v e$
$∴ α < 0 b u t | α | > β ∴ α < 0 < β < | α |$

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