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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.

Quadratic Polynomial Inequalities


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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