Polynomial Inequalities

Quadratic Polynomial Inequalities

Find the range of $x$ that satisfies the inequality $x^2-14x+49 \geq 0.$

\text{all real numbers } x \neq 7

\text{all real numbers } x \neq 49

\text{all real numbers } x

x = 7

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by Brilliant Staff

What is the quadratic inequality the solution of which is $x < -4$ or $x > 6?$

x^2+2x-24 > 0

-x^2+2x+24 < 0

-x^2+2x-24 > 0

x^2+2x-24 < 0

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What is the solution to the following quadratic inequality where the constant $a$ is a negative number: $ax^2+12a^2x+32a^3 > 0?$

x < -{4}a \text{ or } x > -{8}a

-{4}a < x < -{8}a

x < {8}a \text{ or } x > {4}a

{8}a < x < {4}a

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If the range of $x$ that satisfies the inequality $ax^2+35x-30 > 0$ can be expressed as $1 < x < b,$ what is $a+b?$

1 3 2 0

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Which of the following integers does NOT satisfy the inequality $-3x^2+8x+35 > 0 ?$

1 -3 -1 0 4

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