2010009501
Level:
B
Find the solution set of the following equation.
\[
x^{4} - 10x^{2} + 9 = 0
\]
\(\left \{-3;-1;1;3\right \}\)
\(\left \{-3;3\right \}\)
\(\left \{-1;1\right \}\)
\(\left \{1;3\right \}\)
Higher degree equations and inequalities
2010009502
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} - 81 = 0
\]
\(\left \{-3;3\right \}\)
\(\left \{-\sqrt{3};\sqrt{3}\right \}\)
\(\left \{-9;9\right \}\)
\(\left \{-3;-\sqrt{3};\sqrt{3};3\right \}\)
2010009503
Level:
B
The following equation has a solution
\(x = 3\). Find
the sum of the remaining real solutions.
\[
x^{3} - 7x -6 = 0
\]
\(-3\)
\(0\)
\(2\)
\(-1\)
2010009504
Level:
B
Find the solution set of the following inequality.
\[
\left (x +2\right )\left (x +1\right )\left (x - 3\right )\leq 0
\]
\((-\infty ;-2] \cup [ -1;3] \)
\((-\infty ;-2] \)
\((-\infty ;-2] \cup [ -1;\infty )\)
\(\{-2;-1;3\}\)
\((-\infty ;3] \)
2010009505
Level:
B
Find the solution set of the following inequality.
\[
x^{4} - 81 > 0
\]
\( \mathbb{R} \setminus [ -3;3 ]\)
\((3;\infty) \)
\((-\infty ;-3] \cup [ 3;\infty )\)
\((-\infty ;-9) \cup (9;\infty )\)
\((-3;3) \)
2010009506
Level:
B
Find the solution set of the following inequality.
\[
x^{4} +16 \leq 0
\]
\( \emptyset \)
\(\{ -2;2\}\)
\( [-2;2 ] \)
\((-\infty ;-2] \cup [ 2;\infty )\)
\(\mathbb{R}\)
2010009601
Level:
B
Find the solution set of the following inequality.
\[
-x^{3} -3x > 0
\]
\((-\infty ;0) \)
\((3;\infty) \)
\((-\infty ;3) \)
\(\emptyset \)
\((0;\infty) \)
2010009602
Level:
B
Find the sum of the solutions of the following equation.
\[
4(2x -5)(3x^{2} - 2x - 1) = 0
\]
\( \frac{19}6 \)
\( \frac{16}{15} \)
\( \frac{11}6 \)
\( \frac{9}2 \)
2010009603
Level:
B
Find the solution set of the following inequality.
\[
1-x^{3} \geq 0
\]
\((-\infty ;1 ] \)
\((-\infty ;-1 ] \)
\((-\infty ;0 ] \)
\([ 1;\infty) \)
2010009604
Level:
B
Find the solution set of the inequality.
\[ \left(x^6+2\right)\left(x^2+1\right) > 0 \]
\( \mathbb{R} \)
\(( 1;\infty) \)
\(( -1;\infty) \)
\(( 0;\infty) \)