The set of values of m for which the roots of the equation $x^{2} - (m + 1) x + m + 4 = 0$ are real and negative consists of all m such that

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Solution

The correct option is B
$\Rightarrow (m + 1)^{2} - 4 (m + 4) \geq 0$
$\Rightarrow (m - 1)^{2} \geq 4^{2} \Rightarrow\geq 4$
$\Rightarrow m - 1 \leq - 4 o r m - 1 \leq 4$
$\Rightarrow m \leq - 3$ or $m \geq 5$
$∴$ Their product > 0, i.e., m + 4 > 0
$\Rightarrow m > - 4$ . Hence, $- 4 < m \leq - 3$

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