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
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$(5,6]$
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$(6, \infty)$
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$(-\infty, 4)$
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$[4,5]$
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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