Section 1.6 Polynomial and Rational Inequalities.

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Presentation transcript:

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 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.

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,∞)

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

Solve the Inequality Solution:

x 2 – 2x ≥ 1 Solution:

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

Solve the rational inequality Restrictions?

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

Test any number… it’s either all positive, or all negative.

Restrictions? Solve

No Restrictions

Solve Restrictions?