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# Polynomial Inequalities

When does revenue exceed cost? When will one race car pass another? Model these values with polynomials and use polynomial inequalities to solve questions like these and more.

#### Challenge Quizzes

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

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

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

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

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

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