A | math4u.vsb.cz

2010009707

Level:

Find the factored form of the equation. \[ x^4-81=0 \]

\( \left(x^2+9\right)\left(x-3\right)\left(x+3\right)=0 \)

\( \left(x-3\right)^2\left(x+3\right)^2=0 \)

\( \left(x-3\right)^4=0 \)

\( \left(x+9\right)\left(x-3\right)\left(x+3\right)=0 \)

2010009706

Level:

Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once. \[ \left(x^3+8\right)\left(x^2-1\right)=0 \]

\( 1\)

\( -1\)

\( 3\)

\( 0\)

2010009705

Level:

Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once. \[ \left(x^2+1\right)\left(x^2-16 \right)=0 \]

\( 4\)

\( 3\)

\( 5\)

\( 0\)

2010009704

Level:

Find the sum of all real solutions of the following equation. \[ \left (2 - x\right )\left (x^{2} - 9\right ) = 0 \]

\( 2\)

\( 0\)

\( 5\)

\( 3\)

2010009703

Level:

In the following list identify a true statement on the function \(f\). \[ f(x) = (x + 3)(x -1)(x - 2) \]

\(f(x) > 0 \iff x\in (-3;1)\cup (2;\infty)\)

\(f(x) > 0 \iff x\in (-2;-1)\cup (3;\infty)\)

\(f(x) > 0 \iff x\in (-\infty ;-3)\cup (1;2)\)

\(f(x) < 0 \iff x\in (-3;1)\cup (2;\infty)\)

2010009702

Level:

Assuming \(x\in \mathbb{N}\), find the solution set of the following equation. \[ 3 x^{3} - 2x^{2} = 0 \]

\(\emptyset \)

\(\left \{0\right \}\)

\(\left \{\frac23\right \}\)

\(\left \{0;\frac23\right \}\)

2010009701

Level:

Assuming \(x\in \mathbb{N}\), find the solution set of the following equation. \[ x^{3} - 8x^{2} + 16x = 0 \]

\(\left \{4\right \}\)

\(\emptyset \)

\(\left \{0;4\right \}\)

\(\left \{-4;4\right \}\)

2000009408

Level:

Choose a false statement.

\( 2^4\cdot 4^2 > 2^3\cdot 4^3\)

\(3^8=9^4\)

\( \sqrt{3} + \sqrt{6} > \sqrt{3+6}\)

\(\sqrt{2}\cdot \sqrt{2} = \sqrt{2+2}\)

2000009407

Level:

For \(x \in \mathbb{R}\), \(x \neq 0\), simplify the expression \( \frac{x^{-3}x^4}{(x^{-2})^3}\).

\(x^7\)

\(x^2\)

\(1\)

\(x^{-5}\)

2000009406

Level:

For \(x\), \(a\), \(b \in \mathbb{R}\), \(x>0\), simplify the expression \( \sqrt{\frac{x^{a-b}}{x^{b-a}}}\).

\(x^{a-b}\)

\(x^{-\frac12}\)

\(1\)

\(-1\)

« first
‹ previous
…
29
30
31
32
33
34
35
36
37
…
next ›
last »

A

2010009707

2010009706

2010009705

2010009704

2010009703

2010009702

2010009701

2000009408

2000009407

2000009406

Events

Akce

Interests

Zajímavosti

About portal

O portálu