InterviewSolution
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InterviewSolution
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Consider equation `x^(4)-6x^(3)+8x^(2)+4ax-4a^(2)=0,ainR`. Then match the following lists: A. `{:(,a,b,c,d),((1),q,s,s,r):}`B. `{:(,a,b,c,d),((2),r,s,q,p):}`C. `{:(,a,b,c,d),((3),q,s,r,p):}`D. `{:(,a,b,c,d),((4),q,r,p,p):}` |
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Answer» Correct Answer - 4 `(x^(2)-2x-2a)(x^(2)-4x+2a)=0` `impliesx^(2)-2x-2a=0" "....(1)` or `x^(2)-4x+2a=0" "....(2)` Discrtiminant of eq. (1) is: `D_(1)=4+8a` Discriminant of eq. (2) is: `D_(2)=16-8a` (a) If equation has exactly two distinct roots then (1) `D_(1)gt0implies4+8agt0impliesagt-1//2` and `D_(2)implies16-8agt0impliesalt2` `:.ain(-1//2,2)` (b) If equation has exactly two distinct roots then (i) `D_(1)gt0andD_(2)lt0` `impliesain(2,oo)` (ii) `D_(1)lt0andD_(2)gt0` `impliesain(-oo,-1//2)` (c) If equation has no real roots then `D_(1)lt0andD_(2)lt0` `impliesainphi` (d) Clearly, rquation cannot have four roots positive. |
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