kyotsu-test 2014 QCourse1-III

kyotsu-test · Japan · eju-math__session2 Inequalities Simultaneous/Compound Quadratic Inequalities
For each of $\mathbf{A} \sim \mathbf{D}$ in the following questions, choose the correct answer from among (0) $\sim$ (5) below each question.
Consider the three quadratic inequalities
$$\begin{aligned} x ^ { 2 } + 3 x - 18 & < 0 \tag{1}\\ x ^ { 2 } - 2 x - 8 & > 0 \tag{2}\\ x ^ { 2 } + a x + b & < 0 . \tag{3} \end{aligned}$$
(1) The range of $x$ which satisfies both of the inequalities (1) and (2) is $\mathbf { A }$. Also, the range of $x$ which satisfies neither inequality (1) nor (2) is $\mathbf{B}$. (0) $3 \leqq x \leqq 4$
(1) $- 6 \leqq x \leqq - 2$
(2) $3 < x < 4$
(3) $2 < x < 6$
(4) $- 6 < x < - 2$
(5) $- 4 \leqq x \leqq - 3$
(2) The range of $x$ that satisfies at least one of the inequalities (1) and (3) will be $- 6 < x < 7$, if and only if $a$ and $b$ satisfy the equation $\square \mathbf{C}$, and $a$ satisfies the inequality $\square \mathbf{D}$. (0) $b = 6 a - 36$
(1) $b = 7 a - 49$
(2) $b = - 7 a - 49$
(3) $- 10 < a \leqq - 3$
(4) $- 10 < a \leqq - 1$
(5) $- 1 \leqq a < 3$
For each of $\mathbf{A} \sim \mathbf{D}$ in the following questions, choose the correct answer from among (0) $\sim$ (5) below each question.

Consider the three quadratic inequalities

$$\begin{aligned}
x ^ { 2 } + 3 x - 18 & < 0 \tag{1}\\
x ^ { 2 } - 2 x - 8 & > 0 \tag{2}\\
x ^ { 2 } + a x + b & < 0 . \tag{3}
\end{aligned}$$

(1) The range of $x$ which satisfies both of the inequalities (1) and (2) is $\mathbf { A }$. Also, the range of $x$ which satisfies neither inequality (1) nor (2) is $\mathbf{B}$.\\
(0) $3 \leqq x \leqq 4$\\
(1) $- 6 \leqq x \leqq - 2$\\
(2) $3 < x < 4$\\
(3) $2 < x < 6$\\
(4) $- 6 < x < - 2$\\
(5) $- 4 \leqq x \leqq - 3$\\
(2) The range of $x$ that satisfies at least one of the inequalities (1) and (3) will be $- 6 < x < 7$, if and only if $a$ and $b$ satisfy the equation $\square \mathbf{C}$, and $a$ satisfies the inequality $\square \mathbf{D}$.\\
(0) $b = 6 a - 36$\\
(1) $b = 7 a - 49$\\
(2) $b = - 7 a - 49$\\
(3) $- 10 < a \leqq - 3$\\
(4) $- 10 < a \leqq - 1$\\
(5) $- 1 \leqq a < 3$