2000003607
Level:
B
Use the picture to find the solution set of the inequality.
\[
x^3 > x^6
\]
\( (0;1) \)
\( (-\infty; 1 ) \)
\( (1; \infty)\)
\( (-\infty;-1)\)
Higher degree equations and inequalities
2000003606
Level:
B
Use the picture to find the solution set of the inequality.
\[
x^4 < x^2
\]
\( (-1;0) \cup (0;1) \)
\( \emptyset \)
\( (-1;1) \)
\( (-\infty;-1) \)
2000003605
Level:
B
Use the picture to find the solution set of the inequality.
\[
1-x^2 \geq x^2-1
\]
\( [ -1;1 ] \)
\( [ -1;0) \cup (0;1] \)
\( (-\infty ;-1 ] \cup [ 1 ;\infty) \)
\( \{-1;0;1\}\)
2000003604
Level:
B
Find the solution set of the inequality.
\[
(x^2-1)(x^2+1)>0
\]
\( (-\infty;-1) \cup (1;\infty) \)
\( (-1;1)\)
\( (1;\infty) \)
\( (-1;\infty) \)
2000003603
Level:
B
Find the solution set of the inequality.
\[
(x^2+1)x^2< 0
\]
\( \emptyset\)
\( \{0\} \)
\( (-1;1)\)
\( (-1;0) \cup (0;1) \)
2000003602
Level:
B
Find the solution set of the inequality.
\[ x^2+1 < 0\]
\( \emptyset\)
\( (-\infty;-1) \)
\( (-1;1) \)
\( (-\infty;1) \)
2000003601
Level:
B
Find the solution set of the inequality.
\[ x^2 >1 \]
\( (-\infty;-1) \cup (1;\infty) \)
\( (-\infty;-1 ] \cup [ 1;\infty) \)
\( (1;\infty) \)
\( (-1;\infty) \)
1003189109
Level:
A
Find the sum of all the positive roots of the following equation.
\[ 16x^5-9x^3-16x^2+9=0 \]
\( \frac74 \)
\( 1 \)
\( \frac34 \)
\( 0 \)
1003189108
Level:
A
Find the product of all the real roots of the following equation.
\[ 5x^5-3x^3-5x^2+3=0 \]
\( -\frac35 \)
\( \frac53 \)
\( 0 \)
\( 1 \)
1003189107
Level:
A
Given \( x\in\mathbb{R} \), find the solution set of the following equation.
\[ -x^4+x^3-x^2+x=0 \]
Hint: Decompose the polynomial on the left side of the equation into factors.
\( \{ 0;1 \} \)
\( \{-1;0\} \)
\( \{-1;0;1\} \)
\( \{-1;1\} \)