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If a and β (α < β) are the roots of the equation x2 + bx + c = 0 , where c < 0 < b, then : (A) 0 < α < β (B) α < 0 < β < ¦α¦ (C) α < β < 0 (D) α < 0 < ¦α¦< β
let α, β be roots ,
α + β = -b and α*β = c
as c<o and b>0 i.e., -b<0
α.β < 0 and α+β<0
so both α , β must be negative .
as α < β , so the answer is : 0 < α < β
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regards
Ramesh
Option b is right.
Let the roots be p and q. We have p+q<0 and pq<0. This means p<0 and q>0. p+q<0 means q<-p = |p|
Hence we have p<0<q<|p|
we have Alpha + beta = -b ; alpha*beta = c
As c<0 and b>0 ,we get alpha<0<beta
also Beta = -beta - alpha < - alpha = |Alpha|
thus alpha < 0 < beta < |Alpha|
therefore B is the right option
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