SOLVING POLYNOMIAL INEQUALITIES
INTRODUCTION
polynomial inequality:
an inequality that contains a polynomial expression
ex. x3 – 2x2 + 5x + 20  0
To solve a polynomial inequality means to find the interval
of x-values for which the inequality is true.
SOLVING POLYNOMIAL INEQUALITIES
A.
GRAPHICALLY
Ex.
B.
Solve the inequality: 2x(x – 1)(2x + 1)(x + 2) > 0
ALGEBRAICALLY
Ex. 
When are the zeros
included in the
solution set?
Solve the inequality: x2 – 4x + 3 ≥ 0
Steps for Solving a Polynomial Inequality Algebraically:




Determine the roots of the corresponding polynomial equation.
Use the roots to divide the domain into intervals.
Consider the sign of the polynomial in each of the intervals (factor table).
The solution set is determined by the interval(s) that satisfy the given domain.
Ex. 
Solve the inequality: x3 – 3x2 + 4x + 10 < 2x2 + 6x – 14
Ex. 
Target-shooting disks are launched into the air from a machine. The height,
h(t), in metres, of the disk after launch is modelled by the function,
h(t) = –5t2 + 30t + 12, where t is the time in seconds, t ϵ [0, 6.4].
Determine the time interval for which the height of the disk is less than 37m.
Homework: p.226–228 #5, 6ad, 7, 8, 10, 14