If both roots of the Quadratic equation $x^{2} - 2 k x + k^{2} + k - 5 = 0$ are less than 5, then k lies in the interval

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$[4, 6]$

$(6, \infty)$

$(5, 6]$

$(- \infty, 4)$

answer is C.

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Detailed Solution

$f (s) > 0$
$\begin{array}{l} k^{2} - 9 k + 20 > 0 \\ (k - 4) (k - 5) > 0 \\ k \in (- 8, 4) \cup (5, \infty) - - - - - (1) \end{array}$
$\begin{array}{l} - \frac{b}{a} < 5 \\ k < 5 - - - - - (2) \\ ∴ k \in (- \infty, 4) \end{array}$

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