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Algebra

Polynomial Inequalities

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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