9000028303
Level:
B
The following equation has a solution
\(x = -2\). Find
the sum of the remaining real solutions.
\[
x^{3} + 3x^{2} - 18x - 40 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(4\)
Higher degree equations and inequalities
9000028307
Level:
B
Solve the following equation.
\[
x^{3} + 6x^{2} - 8x = 0
\]
\(0\),
\(- 3 -\sqrt{17}\),
\(- 3 + \sqrt{17}\)
\(0\),
\(3 -\sqrt{17}\),
\(3 + \sqrt{17}\)
\(0\),
\(- 3\),
\(\sqrt{
17}\)
\(0\),
\(3\),
\(-\sqrt{17}\)
9000028308
Level:
B
Solve the following equation.
\[
x^{4} - 20x^{2} + 99 = 0
\]
\(-\sqrt{11}\),
\(- 3\),
\(3\),
\(\sqrt{
11}\)
\(0\),
\(- 3 -\sqrt{17}\),
\(- 3 + \sqrt{17}\)
\(0\),
\(3 -\sqrt{17}\),
\(3 + \sqrt{17}\)
\(-\sqrt{17}\),
\(- 3\),
\(3\),
\(\sqrt{
17}\)
9000028310
Level:
B
Find the sum of all real solutions of the following equation.
\[
x^{4} - 20x^{2} + 64 = 0
\]
\(0\)
\(- 10\)
\(4\)
\(10\)
9000029301
Level:
B
Find the solution set of the following inequality.
\[
\left (x - 1\right )\left (x - 2\right )\left (x - 3\right )\geq 0
\]
\(\left [ 1;2\right ] \cup \left [ 3;\infty \right )\)
\(\left (-\infty ;\infty \right )\)
\(\left (-\infty ;1\right )\cup \left (2;3\right )\)
\(\emptyset \)
\(\{0\}\)
9000029302
Level:
B
Find the solution set of the following inequality.
\[
x^{4} - 16 > 0
\]
\(\mathbb{R}\setminus \left [ -2;2\right ] \)
\(\mathbb{R}\)
\(\left (-\infty ;-4\right )\cup \left (4;\infty \right )\)
\(\left (-2;2\right )\)
\(\left (-4;4\right )\)
9000029303
Level:
B
In the following list identify an inequality which does not have solution in
\(\mathbb{R}\).
\(x^{4} + 81 < 0\)
\((x - 3)^{3} > 0\)
\(x^{3} - 9x < 0\)
\(4x^{4} - 64 > 0\)
9000029304
Level:
B
Find the solution set of the following inequality.
\[
x^{3} - 3x^{2} + 2x\geq 0
\]
\(\left [ 0;1\right ] \cup \left [ 2;\infty \right )\)
\(\mathbb{R}\)
\(\emptyset \)
\(\left (-\infty ;0\right ] \cup \left [ 1;2\right ] \)
9000029305
Level:
B
Find the solution set of the following inequality.
\[
x^{4} + 81\leq 0
\]
\(\emptyset \)
\(0\)
\(\mathbb{R}\setminus \left (-9;9\right )\)
\(\mathbb{R}\)
\(\left (-\infty ;-3\right ] \cup \left [ 3;\infty \right )\)
9000029307
Level:
B
In the following list identify an inequality which holds for every
\(x\in \mathbb{R}\).
\(- x^{4} - x^{2}\leq 0\)
\(x^{3} + 3x^{2} + 3x + 1 > 0\)
\(x^{4} + x^{2} + 1 < 0\)
\(- x^{3} + 6x^{2} - 12x + 8 > 0\)