1003067807
Level:
C
Find the solution set of the following equation.
\[ 2x^2+ 4x - 30=\left|2 x^2+ 4 x - 30\right| \]
\( (-\infty;-5]\cup[3;\infty) \)
\( [-5;3] \)
\( (-\infty;-3]\cup[5;\infty) \)
\( [-3;5] \)
Quadratic equations and inequalities
1003067806
Level:
C
Find the solution set of the following equation.
\[ |(x-1)(x+2)|=4 \]
\( \{ -3; 2 \} \)
\( \{ 2 \} \)
\( \{ -2; 3 \} \)
\( \{ -2 \} \)
1003067805
Level:
C
For \( x\in[-3;5] \) find the solution set of the following equation.
\[ \left|(x+3)(x-5)\right|=5 \]
\( \left\{ 1-\sqrt{11};1+\sqrt{11} \right\} \)
\( \left\{ 1-\sqrt{21};1+\sqrt{21} \right\} \)
\( \{ -3; 5 \} \)
\( \left\{1-\sqrt{21}; 1-\sqrt{11};1+\sqrt{11};1+\sqrt{21} \right\} \)
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.
\( x^2-3x-4=2x^2-11x+12 \)
\( x^2-3x-4=-2x^2+11x-12 \)
\(-x^2+3x+4=2x^2-11x+12 \)
\( -x^2+3x+4=-2x^2+11x-12 \)
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.
\( -2x^2+5x+7=-x^2+3x-1 \)
\( 2x^2-5x-7=-x^2+3x-1 \)
\( 2x^2+5x+7=x^2-3x+1 \)
\( -2x^2+5x+7=x^2-3x+1 \)
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.
\( x^2-9x+20=1 \)
\( -x^2+9x-20=1 \)
\( x^2-9x+20=-1 \)
\( x^2+9x-20=1 \)
1003047001
Level:
A
We are given the equation \( 2x^2+10x=8x+2x^2 \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 2x+10=8+2x \)
\( 10x=8x \)
\( 2x^2+2x=2x^2 \)
\( x^2+5x=4x+x^2 \)
1003020001
Level:
A
Find the sum of the roots of the equation.
\[
4x^2+2x=0
\]
\(-\frac12\)
\(0\)
\(2\)
\(-2\)
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.
\(x\in \mathbb{R}\)
9000034909
Level:
B
Find the solution set of the following quadratic inequality.
\[
-3(x + 2)^{2} < 0
\]
\(\mathbb{R}\setminus \{ - 2\}\)
\(\emptyset \)
\(\{- 2\}\)
\(\mathbb{R}\)