Higher Degree Equations and Inequalities

2000003805

Level:

Assuming \(x\in \mathbb{R}\), find the solution set of the following equation. \[ (x^2-9)(2x-5)=0 \]

\( \left\{ -3,\frac{5}{2},3\right\}\)

\( \left\{ \frac{5}{2},3\right\}\)

\( \left\{ \frac{2}{5},3\right\}\)

\( \left\{ -3,\frac{2}{5},3\right\}\)

2010009701

Level:

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

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

\(\emptyset \)

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

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

2010009702

Level:

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

\(\emptyset \)

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

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

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

2010009703

Level:

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

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

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

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

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

2010009704

Level:

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

\( 2\)

\( 0\)

\( 5\)

\( 3\)

2010009705

Level:

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

\( 4\)

\( 3\)

\( 5\)

\( 0\)

2010009706

Level:

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

\( 1\)

\( -1\)

\( 3\)

\( 0\)

2010009707

Level:

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

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

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

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

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

9000019801

Level:

Assuming \(x\in \mathbb{N}\), find the solution set of the following equation. \[ x^{3} - 6x^{2} + 9x = 0 \]

\(\left \{3\right \}\)

\(\emptyset \)

\(\left \{0,3\right \}\)

\(\left \{-3,3\right \}\)

9000019802

Level:

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

\(\emptyset \)

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

\(\left \{2\right \}\)

\(\left \{0, \frac{3} {2}\right \}\)

Higher Degree Equations and Inequalities

2000003805

2010009701

2010009702

2010009703

2010009704

2010009705

2010009706

2010009707

9000019801

9000019802

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