question_answer

If both the roots of the quadratic equation\[{{x}^{2}}-2kx+{{k}^{2}}+k-5=0\]are less than 5, then k lies in the interval     AIEEE  Solved  Paper-2005

A) [4, 5]                     

B) \[(-\infty ,4)\]   

C)        \[(6,\infty )\]               

D)        (5, 6]

Correct Answer: B

Solution :

If both roots ofare less than thenand Let                                                         ...(i) Also,                                          ...(ii) and                                                 and                       ...(iii) From Eqs. (i) and (iii), we get Alternate Solution The given equation is \[{{x}^{2}}-2kx+{{k}^{2}}+k-5=0\] Roots are less than 5. i.e.,                                      ?.(i) But                                 (ii) From Eq.(i),                                                      Either,and                         ...(iii) orand                                  ?.(iv) From Eqs. (ii) and (iv),