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- 1. Quadratic Inequalities
- 2. Quadratic Inequalities It is an inequality of the form of ax2 + bx + c (<, >, ≤, ≥) 0, where a, b and c are real numbers and a ≠ 0
- 3. Quadratic Inequalities Example: x2 + x – 6 = 0 Solution: The left side of the equation can be factored
- 4. Example: x2 + x – 6 = 0 (x + 3) (x-2) > 0 The inequality states that the product of x + 3 and x – 2 is positive. If both factors are positive or both negative, the product is positive
- 5. Value Where On the Number Line x + 3 = 0 If x = -3 Put a 0 above –3 x + 3 > 0 If x > -3 Put + signs to the right of -3 x + 3 < 0 If x < -3 Put – signs to the left of -3 Value Where On the Number Line x + 2 = 0 If x = -2 Put a 0 above –2 x + 2 > 0 If x > -2 Put + signs to the right of -2 x + 2 < 0 If x < -2 Put – signs to the left of -2
- 6. x – 2 - - - - - - - - + + + + + x + 3 - - - 0 + + + + 0 + + + + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 We can see from the sign graph that the product is positive if x <-3 and also positive if x > 2. Positive product since both factors are negative Positive product since both factors are positive
- 7. Steps in solving a Quadratic Inequality with a sign Graph 1. Write the inequality with 0 on the right side 2. Factor the quadratic trinomial 3. Prepare a sign graph showing where each factor is positive, negative, or zero 4. Use the rules for multiplying signed numbers to determine which regions satisfy the original inequality
- 8. 3𝑥 − 4 𝑥 − 2 ≥ 2 3𝑥 − 3 𝑥 + 4 ≤ 0 These inequalities are called Rational inequalities

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