• # 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 2005] A) $(-\infty ,\,4)$ B) [4, 5] C) (5, 6] D) (6, $\infty$)

${{x}^{2}}-2kx+{{k}^{2}}+k-5=0$ 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), $k\in (-\infty ,\,4)$