A) \[(-\infty ,\,4)\]
B) [4, 5]
C) (5, 6]
D) (6, \[\infty \])
Correct Answer: A
Solution :
\[{{x}^{2}}-2kx+{{k}^{2}}+k-5=0\] Roots are less than 5, \[D\ge 0\] \[4{{k}^{2}}-4\,({{k}^{2}}+k-5)\ge 0\] ??(i) Þ \[k\le 5\] Þ \[f(5)>0\] .....(ii) Þ \[k\in (-\infty ,\,4)\cup (5,\infty )\]; \[-\left( \frac{2k}{2} \right)<5\Rightarrow k<5\] ?..(iii) form (i), (ii) and (iii), \[k\in (-\infty ,\,4)\]You need to login to perform this action.
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