9000019806
Level:
B
Find the smallest integer solution of the following equation.
\[
x^{4} - 2x^{3} - x^{2} + 2x = 0
\]
\(- 1\)
\(0\)
\(1\)
\(2\)
B
9000018003
Level:
B
Assuming \(x\in \left (0,3\right ] \),
solve the following inequality.
\[
6 - 2x\leq 3x - 4
\]
\(x\in \left [ 2,3\right ] \)
\(x\in \left (0,3\right ] \)
\(x\in \left (0,2\right ] \)
\(x\in \left (0,\infty \right )\)
9000014209
Level:
B
Consider the function \(f(x) = \frac{3x+1}
{x-2} \).
Find all \(x\)
such that \(f(x) > 0\).
\(x\in \left (-\infty ,-\frac{1}
{3}\right )\cup (2,\infty )\)
\(x\in \left (-\frac{1}
{3},\infty \right )\)
\(x\in (2,3)\)
\(x\in (-\infty ,-3)\cup (2,\infty )\)
9000019809
Level:
B
Find the factorization of the following equation.
\[
x^{3} + 3x^{2} - x - 3 = 0
\]
\(\left (x + 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x - 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x + 1\right ) = 0\)
9000018006
Level:
B
Assuming negative integer \(x\),
solve the following inequality:
\[
x - 2 > 1 - x - 8
\]
\(x\in \left \{-2,-1\right \}\)
\(x\in \left \{-3,-2,-1\right \}\)
\(x\in \left \{-3,-2\right \}\)
\(x\in \left \{-1\right \}\)
9000014210
Level:
B
Consider the function \(f(x) = \frac{2x+1}
{x+3} \).
Find all \(x\)
such that \(f(x) < 0\).
\(x\in \left (-3,-\frac{1}
{2}\right )\)
\(x\in (-\infty ,-3)\cup \left (\frac{1}
{2},\infty \right )\)
\(x\in (-3,\infty )\)
\(x\in \left (-\infty ,-\frac{1}
{2}\right )\)
9000019810
Level:
B
Find the factorization of the following equation.
\[
5x^{4} - 30x^{2} + 40 = 0
\]
\(5\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right )\left (x + 2\right ) = 0\)
\(\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right )\left (x + 2\right ) = 0\)
\(5x\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right ) = 0\)
\(5x\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x + 2\right ) = 0\)
9000018101
Level:
B
Solve the following inequality:
\[
7 -\left (4x - 1\right ) < 3\left (x + 4\right )
\]
\(x\in \left (-\frac{4}
{7},\infty \right )\)
\(x\in \left (-\infty , \frac{4}
{7}\right )\)
\(x\in \left (\frac{4}
{7},\infty \right )\)
\(x\in \left (-\infty ,-\frac{4}
{7}\right )\)
9000019808
Level:
B
Assuming \(x\in \mathbb{C}\),
find the solution set of the following equation.
\[
x\left (x + 1\right )\left (x^{2} + 1\right ) = 0
\]
\(\left \{-1,0,-\mathrm{i},\mathrm{i}\right \}\)
\(\left \{-1,0,1,-\mathrm{i},\mathrm{i}\right \}\)
\(\left \{-1,1,-\mathrm{i},\mathrm{i}\right \}\)
\(\left \{-1,0,-\mathrm{i}\right \}\)
9000018105
Level:
B
Find all the values of \(x\)
which ensure that the following fraction is positive.
\[
- \frac{3}
{5 - 2x}
\]
\(x > \frac{5}
{2}\)
\(x < \frac{5}
{2}\)
\(x < -\frac{5}
{2}\)
\(x > -\frac{5}
{2}\)