9000029303
Level:
B
In the following list identify an inequality which does not have solution in
\(\mathbb{R}\).
\(x^{4} + 81 < 0\)
\((x - 3)^{3} > 0\)
\(x^{3} - 9x < 0\)
\(4x^{4} - 64 > 0\)
B
9000029309
Level:
B
Find the solution set of the following inequality.
\[
(x - 1)(x - 2)(x - 3) < (x - 1)(x - 2)
\]
\((-\infty ,1)\cup (2,4)\)
\(\emptyset \)
\((0,3)\)
\((-\infty ,-3)\cup (3,\infty )\)
\((-3,3)\)
9000029307
Level:
B
In the following list identify an inequality which holds for every
\(x\in \mathbb{R}\).
\(- x^{4} - x^{2}\leq 0\)
\(x^{3} + 3x^{2} + 3x + 1 > 0\)
\(x^{4} + x^{2} + 1 < 0\)
\(- x^{3} + 6x^{2} - 12x + 8 > 0\)
9000029310
Level:
B
Find the solution set of the following inequality.
\[
(x + 2)(x^{2} + 4x + 3) > x^{2} + 5x + 6
\]
\((-3,-2)\cup (0,\infty )\)
\((-\infty ,-3)\cup (3,\infty )\)
\((-\infty ,-1)\cup (1,\infty )\)
\((-1,1)\)
\(\mathbb{R}\)
9000031001
Level:
B
Find the sum of all real roots of the following equation.
\[
(3x - 1)(2x + 1)(4x^{2} + 3x - 1) = 0
\]
\(-\frac{11}
{12}\)
\(- \frac{1}
{12}\)
\(-\frac{1}
{6}\)
\(\frac{1}
{6}\)
9000031002
Level:
B
One of the solutions of the following equation is
\(x = 2\). Find
the set of all solutions.
\[
x^{3} + 2x^{2} - 5x - 6 = 0
\]
\(\{ - 3,-1,2\}\)
\( \{ - 3,-1\}\)
\( \{ - 3,0,2\}\)
\(\{ - 1,2,3\}\)
9000031004
Level:
B
Assuming \(y\in \mathbb{R}\),
find the number of the solutions of the following algebraic equation.
\[
y^{4} + 5y^{2} + 6 = 0
\]
\(0\)
\(4\)
\(3\)
\(2\)
9000031003
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following algebraic equation.
\[
x^{4} + 4x^{2} - 5 = 0
\]
\( \{ - 1,1\}\)
\( \{1\}\)
\( \{ -\sqrt{5},-1,1,\sqrt{5}\}\)
\( \emptyset \)
9000028101
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x) > g(x)\).
\((1,\infty )\)
\(\mathbb{R}\)
\((0,1)\)
\((-\infty ,1)\)
9000028103
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x) > g(x)\).
\((-\infty ,-2)\)
\(\emptyset \)
\((-4,2)\)
\((-2,\infty )\)