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),