A) \[({{a}^{2}},{{a}^{2}}+{{m}^{2}})\]
B) \[({{a}^{2}}-{{m}^{2}},{{a}^{2}})\]
C) [\[{{a}^{2}}-{{m}^{2}},{{a}^{2}}\])
D) none of these
Correct Answer: C
Solution :
| [c] Let the roots be \[\alpha \],\[\beta \] |
| \[\therefore \alpha +\beta =-2a\]and \[\alpha \beta \]=b |
| Given, \[\left| \alpha -\beta \right|\le 2m\] |
| or \[{{\left| \alpha -\beta \right|}^{2}}\le {{(2m)}^{2}}\] or\[{{(\alpha +\beta )}^{2}}-4ab\le 4{{m}^{2}}\] or \[4{{a}^{2}}-4b\le 4{{m}^{2}}\] |
| \[\Rightarrow {{a}^{2}}-{{m}^{2}}\le b\]and discriminant \[D>0\]or \[4{{a}^{2}}-4b>0\] |
| \[\Rightarrow {{a}^{2}}-{{m}^{2}}\le b\] and \[b<{{a}^{2}}\]. |
| Hence, \[b\in [{{a}^{2}}-{{m}^{2}},{{a}^{2}}).\] |
You need to login to perform this action.
You will be redirected in
3 sec
