9000034910
Level:
B
Find the solution set of the following quadratic inequality.
\[
(x - 3)^{2}\geq 0
\]
\(\mathbb{R}\)
\(\emptyset \)
\(\mathbb{R}\setminus \{3\}\)
\(\{3\}\)
Quadratic equations and inequalities
9000039004
Level:
B
Find all \(x\) such that the expression \( (x - 1)(x - 7) \) is negative.
\(x\in (1;7)\)
\(x\in (-\infty ;1)\cup (7;+\infty )\)
No such \(x\)
exists.
\(x\in \mathbb{R}\)
1003067802
Level:
C
For \( x\in (-\infty;3) \) choose the correct form of the equation
\[ \left|x^2- 9 x + 20\right|=1 \]
that does not contain an absolute value.
\( x^2-9x+20=1 \)
\( -x^2+9x-20=1 \)
\( x^2-9x+20=-1 \)
\( x^2+9x-20=1 \)
1003067803
Level:
C
For \( x\in(1;2) \) choose the correct form of the equation
\[ \left|2x^2-5x-7\right|=\left|x^2-3x+1\right| \]
that does not contain an absolute value.
\( -2x^2+5x+7=-x^2+3x-1 \)
\( 2x^2-5x-7=-x^2+3x-1 \)
\( 2x^2+5x+7=x^2-3x+1 \)
\( -2x^2+5x+7=x^2-3x+1 \)
1003067804
Level:
C
For \( x\in[4;\infty) \) choose the correct form of the equation
\[ \left|-x^2+3x+4\right|=\left|-2 x^2+ 11 x - 12\right| \]
that does not contain an absolute value.
\( x^2-3x-4=2x^2-11x+12 \)
\( x^2-3x-4=-2x^2+11x-12 \)
\(-x^2+3x+4=2x^2-11x+12 \)
\( -x^2+3x+4=-2x^2+11x-12 \)
1003067805
Level:
C
For \( x\in[-3;5] \) find the solution set of the following equation.
\[ \left|(x+3)(x-5)\right|=5 \]
\( \left\{ 1-\sqrt{11};1+\sqrt{11} \right\} \)
\( \left\{ 1-\sqrt{21};1+\sqrt{21} \right\} \)
\( \{ -3; 5 \} \)
\( \left\{1-\sqrt{21}; 1-\sqrt{11};1+\sqrt{11};1+\sqrt{21} \right\} \)
1003067806
Level:
C
Find the solution set of the following equation.
\[ |(x-1)(x+2)|=4 \]
\( \{ -3; 2 \} \)
\( \{ 2 \} \)
\( \{ -2; 3 \} \)
\( \{ -2 \} \)
1003067807
Level:
C
Find the solution set of the following equation.
\[ 2x^2+ 4x - 30=\left|2 x^2+ 4 x - 30\right| \]
\( (-\infty;-5]\cup[3;\infty) \)
\( [-5;3] \)
\( (-\infty;-3]\cup[5;\infty) \)
\( [-3;5] \)
1003067808
Level:
C
Find the solution set of the following equation.
\[ -2 x^2+ 5 x + 3 =\left|-2 x^2+ 5 x + 3\right| \]
\( \left[-\frac12;3\right] \)
\( [-5;3] \)
\( \left(-\infty;-\frac12\right]\cup[3;\infty) \)
\( (-\infty,-3]\cup[5,\infty) \)
1003067810
Level:
C
Find the solution set of the following equation.
\[ |x-4|\cdot(x+4)=4 \]
\( \left\{-2\sqrt3;2\sqrt3;2\sqrt5\right\} \)
\( \{ -4; 4 \} \)
\( \left\{ -2\sqrt3;2\sqrt3\right\} \)
\( \left\{ 2\sqrt3;2\sqrt5\right\} \)
\( \left\{-2\sqrt5;-2\sqrt3;2\sqrt3;2\sqrt5 \right\} \)