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If both the 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

1) $(5,6]$
2) $(6, \infty)$
3) $(-\infty, 4)$
4) $[4,5]$
in Mathematics by Bronze Status (9,486 points) | 11 views

1 Answer

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$\frac{-b}{2 a}<5$ and $f(5)>0$

$\Rightarrow \frac{2 K}{2}<5$ and $25-10 K+K^{2}+K-5>0$

$\Rightarrow k \in(-\infty, 4)$

by Bronze Status (9,486 points)

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