Question

The set of values of a for which the inequality $x^2+ax+a^2+6a<0$ is satisfied for all $x\in (1,2)$ lies in the interval.

• A. $(1,2)$
• B. $[1,2]$
• C. $[-7,4]$
• D. None of these

Answer 1

The correct option is D None of these

$f\left(x\right)=x^2+ax+a^2+6a$

$f\left(1\right)\le 0\Rightarrow a^{+}7a+1\le 0$

$f\left(2\right)\le 0\Rightarrow a^2+8a+4\le 0$

$a^{+}7a+1\le 0\Rightarrow a=\frac{-7-3\sqrt{5}}{2}$

$a^2+8a+4\le 0\Rightarrow a=-4+2\sqrt{3}$

$\therefore \frac{-7-3\sqrt{5}}{2}\le a\le -4+2\sqrt{3}$