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Question Number 20054 by Tinkutara last updated on 21/Aug/17

If α and β (α < β) are the roots of the

equation x^{2} + b x + c = 0, where

c < 0 < b, then

(1) 0 < α < β

(2) α < 0 < β < ∣ α ∣

(3) α < β < 0

(4) α < 0 < ∣ α ∣ < β

Answered by ajfour last updated on 21/Aug/17

c < 0 < b, α + β = - b, α β = c

\Rightarrow x = \frac{α + β}{2} = \frac{- b}{2} < 0 & α β = c < 0

\Rightarrow α < 0 a n d β > 0

f u r t h e r s i n c e \frac{α + β}{2} < 0, ∣ α ∣> β

s o c o r r e c t o p t i o n i s (2) .

Commented by Tinkutara last updated on 21/Aug/17

Thank you very much Sir!