Higher Degree Equations and Inequalities

1003028902

Level:

Find the factored form of the equation. \[ x^4+2x^2+x^3+2x=0 \]

\( x\left(x^2+2\right)\left(x+1\right)=0 \)

\( x\left(x^2+1\right)\left(x+1\right)=0 \)

\( x\left(x^2+1\right)\left(x+2\right)=0 \)

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

1003028901

Level:

Find the factored form of the equation. \[ x^4-16=0 \]

\( \left(x^2+4\right)\left(x-2\right)\left(x+2\right)=0 \)

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

\( \left(x-2\right)^4=0 \)

\( \left(x+4\right)\left(x-2\right)\left(x+2\right)=0 \)

1003029006

Level:

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

\( \emptyset \)

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

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

\( (-1;1) \)

1003029005

Level:

Find the solution set of the inequality. \[ \left(2x^2-18\right)\left(x^3-8\right) < 0 \]

\( (-\infty;-3)\cup(2;3) \)

\( (-3;2)\cup(3;\infty) \)

\( (-3;3) \)

\( (-\infty;-3) \)

1003029004

Level:

Find the solution set of the inequality. \[ x^4-1\geq0 \]

\( (-\infty;-1]\cup[1;\infty) \)

\( [-1;1] \)

\( \mathbb{R} \)

\( [ 1;\infty ) \)

1003029003

Level:

Find the solution set of the inequality. \[ \left(x^3+8\right)\left(x^4+1\right)\left(x-3\right) < 0 \]

\( (-2;3) \)

\( (-\infty;-2)\cup(3;\infty) \)

\( (-2;\infty) \)

\( (-\infty;-2)\cup(-1;1)\cup(3;\infty) \)

1003029002

Level:

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

\( \left(-\infty;-\sqrt3\right)\cup(-1;1)\cup\left(\sqrt3;\infty\right) \)

\( \left(-\sqrt3;-1\right)\cup\left(1;\sqrt3\right) \)

\( \left(-\infty;-\sqrt3\right)\cup(1;\sqrt3)\cup\left(\sqrt3;\infty\right) \)

\( \left(-\infty;1\right)\cup\left(\sqrt3;\infty\right) \)

1003028806

Level:

Find all the real roots of the equation. \[ \left(x^4-1\right)\left(x^3-8\right)\left(x^2-2\right)=0 \]

\( \left\{-\sqrt2;-1;1;\sqrt2;2\right\} \)

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

\( \left\{-\sqrt2;-1;1;\sqrt2\right\} \)

\( \left\{-\sqrt2;\sqrt2;2\right\} \)

1003028805

Level:

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

\( -2 \)

\( 0 \)

\( 2 \)

\( -3 \)

1003028804

Level:

For the next equation, find the sum of all the roots from the set of natural numbers. Multiple roots, if any, count only once. \[ \left(x^3+1\right)\left(x^2-4\right)=0 \]

\( 2 \)

\( -1 \)

\( 3 \)

\( 1 \)

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Higher Degree Equations and Inequalities

1003028902

1003028901

1003029006

1003029005

1003029004

1003029003

1003029002

1003028806

1003028805

1003028804

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