Quadratic Inequality

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DEFINITION:

A quadratic inequality is an inequality that can be written so that one side is a quadratic expression and the other side is zero.

X^2 – 2x – 3 ≥ 0

X^2 – 2x – 3 ≤ 0

X^2 – 2x – 3 > 0

X^2 – 2x – 3 < 0

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THEOREM:

Let r and s be two real numbers with r < s.

The solution set of

(x-r)(x-s) > 0

SS: {x|x<r or x>s}

The solution set of

(x-r)(x-s) < 0

SS: {x|r<x<s}

The solution set of

(x-r)(x-s) ≥ 0

SS: {x|x ≤ r or x ≥ s}

The solution set of

(x-r)(x-s) ≤ 0

SS: {x|r ≤ x ≤ s}

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SET BUILDER NOTATION:

SS: {x|x<r or x>r}

INTERVAL NOTATION:

(-∞,r) U (s,∞)