Transcript Angles, Degrees, and Special Triangles
Nonlinear Inequalities MATH 109 - Precalculus S. Rook
Overview • Section 2.7 in the textbook: – Solving polynomial inequalities 2
Solving Polynomial Inequalities
Solving Inequalities • • • An inequality is similar to an
equality
except instead of =, we have >, <, ≤ or ≥.
– Essentially solved in the same way as an
equality Solution set
– all values that satisfy an inequality Whereas an
equality
has at most 1 solution, the solution to an inequality is a set – possibly with infinitely many elements 4
Solving Polynomial Inequalities • • • We discussed how to solve polynomial
equalities
Only difference is that the
solution set
consists of
intervals
number now instead of a single real To solve an inequality such as (x + 1)(x – 1) > 0: – By the
Zero Product Principle
, x = -1 or x = 1 – This subdivides the interval (-oo, +oo) into three subintervals: (-oo, -1), (-1, 1), (1, +oo) 5
Solving Polynomial Inequalities (Continued) – Pick one value in each subinterval and test it in the inequality to find the
sign
of that subinterval • Recall the
sign property of polynomials
– The sign in each subinterval is the
SAME
• Keep only those intervals that satisfy the inequality • If more than one interval satisfies the inequality, union them 6
Solving Polynomial Inequalities (Example)
Ex 1:
Write the solution set in interval notation: a) x 2 + 4x + 4 ≥ 9 c) 2x 2 – 7x ≤ -2 b) 3x 2 + 7x < 6 d)
x
3 – 4x > 0 7
Summary • • • After studying these slides, you should be able to: – Solve polynomial inequalities, graph the solution set on a number, and write the solution set in interval notation Additional Practice – See the list of suggested problems for 2.7
Next lesson – Exponential Functions and Their Graphs (Section 3.1) 8