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If a and β (α 2 + bx + c = 0 , where c (A) 0 (C) α

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

Grade:12

3 Answers

Ramesh V
70 Points
12 years ago

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

mycroft holmes
272 Points
12 years ago

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|

Sudheesh Singanamalla
114 Points
11 years ago

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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