2010009702
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
3 x^{3} - 2x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{\frac23\right \}\)
\(\left \{0;\frac23\right \}\)
Higher degree equations and inequalities
2010009701
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
x^{3} - 8x^{2} + 16x = 0
\]
\(\left \{4\right \}\)
\(\emptyset \)
\(\left \{0;4\right \}\)
\(\left \{-4;4\right \}\)
2010009606
Level:
B
Find the solution set of the inequality.
\[ \left(4-x^2\right)\left(x^3+1\right) > 0 \]
\( (-\infty;-2)\cup(-1;2) \)
\( (-\infty;-2)\)
\( (-\infty;2) \)
\( (-\infty;-1)\cup(0;2) \)
2010009605
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following algebraic equation.
\[
x^{4} -3x^{2} - 4 = 0
\]
\( \{ -2;2\} \)
\( \{ 2\} \)
\( \{ -2;-1;1;2\} \)
\( \{ -1;2\} \)
2010009604
Level:
B
Find the solution set of the inequality.
\[ \left(x^6+2\right)\left(x^2+1\right) > 0 \]
\( \mathbb{R} \)
\(( 1;\infty) \)
\(( -1;\infty) \)
\(( 0;\infty) \)
2010009603
Level:
B
Find the solution set of the following inequality.
\[
1-x^{3} \geq 0
\]
\((-\infty ;1 ] \)
\((-\infty ;-1 ] \)
\((-\infty ;0 ] \)
\([ 1;\infty) \)
2010009602
Level:
B
Find the sum of the solutions of the following equation.
\[
4(2x -5)(3x^{2} - 2x - 1) = 0
\]
\( \frac{19}6 \)
\( \frac{16}{15} \)
\( \frac{11}6 \)
\( \frac{9}2 \)
2010009601
Level:
B
Find the solution set of the following inequality.
\[
-x^{3} -3x > 0
\]
\((-\infty ;0) \)
\((3;\infty) \)
\((-\infty ;3) \)
\(\emptyset \)
\((0;\infty) \)
2010009506
Level:
B
Find the solution set of the following inequality.
\[
x^{4} +16 \leq 0
\]
\( \emptyset \)
\(\{ -2;2\}\)
\( [-2;2 ] \)
\((-\infty ;-2] \cup [ 2;\infty )\)
\(\mathbb{R}\)
2010009505
Level:
B
Find the solution set of the following inequality.
\[
x^{4} - 81 > 0
\]
\( \mathbb{R} \setminus [ -3;3 ]\)
\((3;\infty) \)
\((-\infty ;-3] \cup [ 3;\infty )\)
\((-\infty ;-9) \cup (9;\infty )\)
\((-3;3) \)