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Polynomial Inequalities

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

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Polynomial Inequalities

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

  2. Polynomial Inequalities 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…

  3. 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: Negative Positive Positive –3 4 The function is positive on The function is negative on

  4. Polynomial Inequalities Determine the real number values of x that cause the given function to be (a) zero, (b) positive, (c) negative. Negative Positive Positive –3 4 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 ?

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

  6. 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…

  7. Polynomial Inequalities Solve the given inequality analytically. 4 2 –7 –10 24 8 4 –24 2 1 –6 0

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

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

  10. 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

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

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

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