2000001003
Level:
A
Which of the following equations has the solution set \(K=\left\{-\sqrt{3}, \sqrt{3}\right\}\)?
\(3x^2-9=0\)
\(x^2+9=0\)
\(x^2-9x=0\)
\(3x^2-1=0\)
Quadratic Equations and Inequalities
2000001002
Level:
A
Which of the following equations has the solution set \(K=\{0, 10\}\)?
\(x^2-10x=0\)
\(10x^2-x=0\)
\(x^2-10x=10\)
\(x^2+10x=0\)
2000001001
Level:
A
Which of the following equations has the solution set \(K=\{-1, 3\}\)?
\( (x+1)(x-3)=0\)
\( (x-1)(x+3)=0\)
\( 5(x-1)(x+3)=0\)
\( (x+1)(x-3)=1\)
2000000705
Level:
B
Use the given graph of the function \(f: y=(x-2)(x-3)=x^2-5x+6\) to solve the inequality \((x-2)(x-3)< 0\).
\(x \in (2,3)\)
\(x \in \mathbb{R}\setminus \{2,3\}\)
\(x \in (-\infty,2)\cup(3,\infty)\)
\(x \in \emptyset\)
2000000704
Level:
B
Use the given graph of the function \(f: y=-x^2+5x\) to solve the inequality \(-x^2+5x< 0\).
\(x \in (-\infty,0)\cup(5,\infty)\)
\(x \in \mathbb{R}\setminus \{0,5\}\)
\(x \in(0,5)\)
\(x \in (0,6.25)\)
2000000703
Level:
B
Use the given graph of the function \(f: y=x^2-4\) to solve the inequality \(x^2-4< 0\).
\(x \in (-2,2)\)
\(x \in \mathbb{R}\setminus \{-2,2\}\)
\(x \in (-4,0)\)
\(x \in (-\infty,-2) \cup (2,\infty)\)
2000000702
Level:
B
Use the given graph of the function \(f: y=-x^2-1\) to solve the inequality \(-x^2-1\leq 0\).
\(x \in \mathbb{R}\)
\(x \in \emptyset\)
\(x \in (-1,1)\)
\(x \in (-\infty,-1)\cup(1,\infty)\)
2000000701
Level:
B
Use the given graph of the function \(f: y=x^2-2x+1\) to solve the inequality \(x^2-2x+1>0\).
\(x \in \mathbb{R}\setminus \{1\}\)
\(x \in \mathbb{R}\setminus \{-1\}\)
\(x \in \mathbb{R}\)
\(x \in \{1\}\)
2000000205
Level:
B
Solve the following inequality.
\[
-100- x^{2} \leq 0
\]
\(x \in \mathbb{R}\)
\(x \in \mathbb{R}\setminus \{-10,10\}\)
\(x \in \emptyset \)
\(x \in (-10 ,10)\)
2000000204
Level:
B
Solve the following inequality.
\[
(5-x)^{2}\leq 0
\]
\(x \in \{5\}\)
\(x \in \mathbb{R}\setminus \{5\}\)
\(x \in \emptyset \)
\(x \in (-\infty ,-5)\cup (5,\infty )\)