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pallavi pradeep bhardwaj Grade: 12
        

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

7 years ago

Answers : (3)

Ramesh V
70 Points
										

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


--


regards


Ramesh

7 years ago
mycroft holmes
266 Points
										

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|

7 years ago
Sudheesh Singanamalla
114 Points
										

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

6 years ago
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