Polynomial Inequalities The last section in Chapter 2!!! Boo Hoo  2.9a.

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Presentation transcript:

Polynomial Inequalities The last section in Chapter 2!!! Boo Hoo  2.9a

They can be written in the forms: To solve the inequality f (x) > 0 is to find the values of x that make f (x) positive To solve the inequality f (x) < 0 is to find the values of x that make f (x) negative If the expression f (x) is a product, we can find its sign by looking at the sign of each of its factors…

Polynomial Inequalities Determine the real number values of x that cause the given function to be (a) zero, (b) positive, (c) negative. Real zeros: x = –3, 4 We can use a sign chart to find the other values of x: –34 NegativePositive The function is positive on The function is negative on

Polynomial Inequalities Determine the real number values of x that cause the given function to be (a) zero, (b) positive, (c) negative. –34 NegativePositive The function is positive on The function is negative on Does this make sense given the multiplicity of the zeros? Can we verify all of this graphically ?

Polynomial Inequalities For the same function, give the solution of each of the following:

Polynomial Inequalities Solve the given inequality analytically. Let Use the RZT to list the possible rational zeros!!! Look at the graph  x = 4 seems like a good guess…

Polynomial Inequalities Solve the given inequality analytically. 42–7– –24 21–60

Polynomial Inequalities Solve the given inequality analytically. Give the end behavior of this function!!! Zeros: 4, 3/2, –2  all of multiplicity 1!!!

Polynomial Inequalities Solve the given inequality analytically. Now, for the sign chart: –2 Sign Change PositiveNegativex 3/2 Sign Change 4 Sign Change Pos. due to end behavior Neg. due to end behavior Solution:

Polynomial Inequalities Solve the given inequality graphically. Set equal to zero: Rewrite as a function: Graph to find the real zeros and solve the inequality!!! Solution

Polynomial Inequalities with Unusual Answers… Give the solution to each of the following:The graph??? No Solution

Polynomial Inequalities with Unusual Answers… Give the solution to each of the following:The graph??? No Solution