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Section 1.6

Section 1.6. Polynomial and Rational Inequalities. Polynomial Inequalities. We said that we can find the solutions (a.k.a. zeros) of a polynomial by setting the polynomial equal to zero and solving. We are going to use this skill to solve inequalities such as:. Solving Quadratic Inequalities.

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Section 1.6

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  1. Section 1.6 Polynomial and Rational Inequalities

  2. Polynomial Inequalities • We said that we can find the solutions (a.k.a. zeros) of a polynomial by setting the polynomial equal to zero and solving. • We are going to use this skill to solve inequalities such as:

  3. Solving Quadratic Inequalities Factor Identify the zeros (critical points) There are now 3 intervals: (-∞,-3), (-3,4), and (4,∞). We will test these three intervals to see which parts of this function are less than (negative) or greater than (positive) zero.

  4. Testing Intervals • To test, pick a number from each interval and evaluate • Instead of evaluating, we can also just check the signs of each factor in our factored form of the polynomial. Solution: (-∞,-3) U (4,∞)

  5. Recap of Steps • Factor and solve the quadratic to find the critical points • Test each interval • Determine if (+) or (-) values are desired

  6. Solve the Inequality Solution:

  7. x2 – 2x ≥ 1 Solution:

  8. x2 + 2x ≤ -3 No Real Solutions Test any number to find out if all numbers are true or false.

  9. Solving Rational Inequalities Restrictions? -8 -1 8 Solution: (-∞,-8) U (-1,8)

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