Higher Degree Equations and Inequalities

9000019807

Level: 
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation. \[ \left (3x + 2\right )\left (x\sqrt{2} + 1\right )\left (x^{2} + 1\right ) = 0 \]
\(\left \{-\frac{\sqrt{2}} {2} ,-\frac{2} {3}\right \}\)
\(\left \{-\frac{2} {3}, \frac{1} {\sqrt{2}}\right \}\)
\(\left \{\frac{2} {3}, \frac{1} {\sqrt{2}}\right \}\)
\(\left \{-1,-\frac{\sqrt{2}} {2} ,-\frac{2} {3}\right \}\)

9000025805

Level: 
A
In the following list identify a true statement on the function \(f\). \[ f(x) = (x + 1)(x + 2)(x - 3) \]
\(f(x) < 0 \iff x\in (-\infty ,-2)\cup (-1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3} {2}\right )\cup (1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3} {2}\right )\cup (3,\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3} {2},-1\right )\cup (3,\infty )\)

1003029002

Level: 
B
Find the solution set of the inequality. \[ \left(x^2-1\right)\left(x^2-3\right) > 0 \]
\( \left(-\infty,-\sqrt3\right)\cup(-1,1)\cup\left(\sqrt3,\infty\right) \)
\( \left(-\sqrt3,-1\right)\cup\left(1,\sqrt3\right) \)
\( \left(-\infty,-\sqrt3\right)\cup(1,\sqrt3)\cup\left(\sqrt3,\infty\right) \)
\( \left(-\infty,1\right)\cup\left(\sqrt3,\infty\right) \)