If both the roots of the quadratic equation $x^2-2 k x+k^2+k-5=0$ are less than 5 , then $\mathrm{k}$ lies…

If both the roots of the quadratic equation $x^2-2 k x+k^2+k-5=0$ are less than 5 , then $\mathrm{k}$ lies in the interval
  1. $(5,6]$
  2. $(6, \infty)$
  3. $(-\infty, 4)$
  4. $[4,5]$

Solution

$ \begin{aligned} & \frac{-b}{2 a} < 5 \\ & f(5)>0 \\ & \Rightarrow k \in(-\infty, 4) . \end{aligned} $

Asked in: JEE Main 2005

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