Higher degree equations and inequalities

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. \[ x^{3} - 8x^{2} + 16x = 0 \]

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

\(\emptyset \)

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

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

2010009606

Level:

Find the solution set of the inequality. \[ \left(4-x^2\right)\left(x^3+1\right) > 0 \]

\( (-\infty;-2)\cup(-1;2) \)

\( (-\infty;-2)\)

\( (-\infty;2) \)

\( (-\infty;-1)\cup(0;2) \)

2010009605

Level:

Assuming \(x\in \mathbb{R}\), solve the following algebraic equation. \[ x^{4} -3x^{2} - 4 = 0 \]

\( \{ -2;2\} \)

\( \{ 2\} \)

\( \{ -2;-1;1;2\} \)

\( \{ -1;2\} \)

2010009604

Level:

Find the solution set of the inequality. \[ \left(x^6+2\right)\left(x^2+1\right) > 0 \]

\( \mathbb{R} \)

\(( 1;\infty) \)

\(( -1;\infty) \)

\(( 0;\infty) \)

Higher degree equations and inequalities

2010009707

2010009706

2010009705

2010009704

2010009703

2010009702

2010009701

2010009606

2010009605

2010009604

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