Quadratic EquationHard
Question
Complete set of real values of k for which the inequality ${kx}^{2} - kx - 1 < 0$ holds for any real $x$, satisfy
Options
A.$k \in ( - 4,0)$
B.$k \in ( - 4,0\rbrack$
C.$k \in \lbrack - 4,0)$
D.$k \in \lbrack - 4,0\rbrack$
Solution
${kx}^{2} - kx - 1 < 0\forall x \in R$
$k = 0$ holds
Hence,
$$\begin{matrix} \text{~OR~} \\ k < 0\text{~and~}D < 0 \\ k^{2} + 4k < 0 \Rightarrow \ k \in ( - 4,0) \\ k \in ( - 4,0\rbrack \end{matrix}$$
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