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
2000000204
Level:
B
Solve the following inequality.
\[
(5-x)^{2}\leq 0
\]
\(x \in \{5\}\)
\(x \in \mathbb{R}\setminus \{5\}\)
\(x \in \emptyset \)
\(x \in (-\infty ;-5)\cup (5;\infty )\)
2000000205
Level:
B
Solve the following inequality.
\[
-100- x^{2} \leq 0
\]
\(x \in \mathbb{R}\)
\(x \in \mathbb{R}\setminus \{-10;10\}\)
\(x \in \emptyset \)
\(x \in (-10 ;10)\)
2000000701
Level:
B
Use the given graph of the function \(f: y=x^2-2x+1\) to solve the inequality \(x^2-2x+1>0\).
\(x \in \mathbb{R}\setminus \{1\}\)
\(x \in \mathbb{R}\setminus \{-1\}\)
\(x \in \mathbb{R}\)
\(x \in \{1\}\)
2000000702
Level:
B
Use the given graph of the function \(f: y=-x^2-1\) to solve the inequality \(-x^2-1\leq 0\).
\(x \in \mathbb{R}\)
\(x \in \emptyset\)
\(x \in (-1;1)\)
\(x \in (-\infty;-1)\cup(1;\infty)\)
2000000703
Level:
B
Use the given graph of the function \(f: y=x^2-4\) to solve the inequality \(x^2-4< 0\).
\(x \in (-2;2)\)
\(x \in \mathbb{R}\setminus \{-2;2\}\)
\(x \in (-4;0)\)
\(x \in (-\infty;-2) \cup (2;\infty)\)
2000000704
Level:
B
Use the given graph of the function \(f: y=-x^2+5x\) to solve the inequality \(-x^2+5x< 0\).
\(x \in (-\infty;0)\cup(5;\infty)\)
\(x \in \mathbb{R}\setminus \{0;5\}\)
\(x \in(0;5)\)
\(x \in (0;6.25)\)
2000000705
Level:
B
Use the given graph of the function \(f: y=(x-2)(x-3)=x^2-5x+6\) to solve the inequality \((x-2)(x-3)< 0\).
\(x \in (2;3)\)
\(x \in \mathbb{R}\setminus \{2;3\}\)
\(x \in (-\infty;2)\cup(3;\infty)\)
\(x \in \emptyset\)
2010004501
Level:
B
One of the solutions of the quadratic equation \( x^{2} + 7x +c = 0\) is \(x_{1} = -3\). Find the second solution \(x_{2}\) and the value of the coefficient \(c\).
\(x_{2} = -4\) and
\(c = 12\)
\(x_{2} = 4\) and
\(c = -12\)
\(x_{2} = -4\) and
\(c = -12\)
\(x_{2} = 4\) and
\(c = 12\)
2010004502
Level:
B
The quadratic equation
\[
ax^{2} + bx -24 = 0
\]
has solutions \(x_{1} = -2\)
and \(x_{2} = 4\). Find the
coefficients \(a\)
and \(b\).
\(a = 3\),
\(b = -6\)
\(a = -3\),
\(b = -6\)
\(a = -3\),
\(b = 6\)
\(a = 3\),
\(b = 6\)