2000000203
Level:
B
Solve the following inequality.
\[
(x+1)^{2}>0
\]
\(x \in \mathbb{R}\setminus \{-1\}\)
\(x \in \mathbb{R}\setminus \{1\}\)
\(x \in (-1 ;1)\)
\(x \in (-\infty ;-1)\cup (1;\infty )\)
Quadratic equations and inequalities
2000000202
Level:
B
Solve the following inequality.
\[
x^{2} + 9\leq 0
\]
\(x \in \emptyset \)
\(x \in \mathbb{R}\)
\(x \in (-3 ;3)\)
\(x \in (-\infty ;-3)\cup (3;\infty )\)
2000000201
Level:
B
Solve the following inequality.
\[
x^2+1>0
\]
\(x \in \mathbb{R}\)
\(x \in \emptyset \)
\(x \in (-1;1)\)
\(x \in (-\infty ;-1)\cup (1;\infty )\)
Graphical Solution of Inequalities
Submitted by ladislav.foltyn on Fri, 05/10/2019 - 19:351003162910
Level:
C
Find the sum of all the roots of the equation \( \left|x^2+2x\right|-6=|3x| \).
\( -3 \)
\( 9 \)
\( 0 \)
\( -2 \)
1003187313
Level:
C
Which of the given sets contains exactly all negative integers that satisfy the inequality \( \sqrt{(2x-8)^2} < 14 \)?
\( \{-2;-1\} \)
\( \{-3;-2;-1\} \)
\( \{-10;-9;-8;-7;-6;-5;-4;-3;-2;-1\} \)
\( \{-4;-3;-2;-1\} \)
1003124107
Level:
B
Find the roots of the following equation using Vieta’s formulas.
\[ x^2-11x+10=0 \]
\( \{1; 10 \} \)
\( \{ -11; -1\} \)
\( \{1;11 \} \)
\( \{-1; 10 \} \)
1003124106
Level:
B
Find the roots of the following equation using Vieta’s formulas.
\[ x^2-8x+15=0 \]
\( \{3;5\} \)
\( \{ -3;-5\} \)
\( \{-5;3 \} \)
\( \{-3;5 \} \)
1003124105
Level:
B
Find the sum of the roots of the following equation. Use Vieta’s formulas, don’t solve the equation.
\[ x^2-x-12=0 \]
\( 1 \)
\( -1 \)
\( -12 \)
\( 12 \)
1003124104
Level:
B
The following equation has roots \( -3 \) and \( -2 \). Find the value of the constant \( c \).
\[ x^2+bx+c=0 \]
\( 6 \)
\( -3 \)
\( -2 \)
\( -6 \)