Q144 / 225 · JEE Main 2005 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'C'.

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