2010009505
Level:
B
Find the solution set of the following inequality.
\[
x^{4} - 81 > 0
\]
\( \mathbb{R} \setminus [ -3;3 ]\)
\((3;\infty) \)
\((-\infty ;-3] \cup [ 3;\infty )\)
\((-\infty ;-9) \cup (9;\infty )\)
\((-3;3) \)
Higher Degree Equations and Inequalities
2010009504
Level:
B
Find the solution set of the following inequality.
\[
\left (x +2\right )\left (x +1\right )\left (x - 3\right )\leq 0
\]
\((-\infty ;-2] \cup [ -1;3] \)
\((-\infty ;-2] \)
\((-\infty ;-2] \cup [ -1;\infty )\)
\(\{-2;-1;3\}\)
\((-\infty ;3] \)
2010009503
Level:
B
The following equation has a solution
\(x = 3\). Find
the sum of the remaining real solutions.
\[
x^{3} - 7x -6 = 0
\]
\(-3\)
\(0\)
\(2\)
\(-1\)
2010009502
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} - 81 = 0
\]
\(\left \{-3;3\right \}\)
\(\left \{-\sqrt{3};\sqrt{3}\right \}\)
\(\left \{-9;9\right \}\)
\(\left \{-3;-\sqrt{3};\sqrt{3};3\right \}\)
2010009501
Level:
B
Find the solution set of the following equation.
\[
x^{4} - 10x^{2} + 9 = 0
\]
\(\left \{-3;-1;1;3\right \}\)
\(\left \{-3;3\right \}\)
\(\left \{-1;1\right \}\)
\(\left \{1;3\right \}\)
2000003806
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^3+1)(x^2+25)=0
\]
\( \{-1\}\)
\( \{-5;-1\}\)
\( \{-5;-1;1;5\}\)
\( \{-5;-1;5\}\)
2000003805
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^2-9)(2x-5)=0
\]
\( \left\{ -3;\frac{5}{2};3\right\}\)
\( \left\{ \frac{5}{2};3\right\}\)
\( \left\{ \frac{2}{5};3\right\}\)
\( \left\{ -3;\frac{2}{5};3\right\}\)
2000003804
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^3-1)x^2=0
\]
\( \{0;1\}\)
\( \{-1;0;1\}\)
\( \{-1;1\}\)
\( \{-1;0\}\)
2000003803
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^2+1)(x^2-4)=0
\]
\( \{-2;2\}\)
\( \{-2;-1;1;2\}\)
\( \{-2;-1;2\}\)
\( \{-1;2\}\)
2000003802
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^2-1)x=0
\]
\( \{-1;0;1\}\)
\( \{0;1\}\)
\( \{-1;0\}\)
\( \{-1;1\}\)