Warm - Up

•Find the Vertex of f(x) = x2 – 2x + 4

Announcements

•Assignment▫p. 248▫# 25 - 28 ▫p. 291

# 1, 2, 15, 16, 21, 31, 32, 37, 38, 51, 52•Chapter Test 2.1 – 2.4 on Thursday.•Corrections Friday if you have turned in

all of your assignments

2.4 Real Zeros of Polynomial Functions•How to use the Rational Zero Test to determine possible rational zeros of polynomial functions•How to use Descartes’s Rule of Signs

The rational zero test

•Any rational zero of f will be of the form p/q, ▫P = factor of the constant▫Q = factor of the coefficient of term with

highest degree

▫Possible rational zeros?

f(x) = 2x3 – x2 + x + 4

Example 6. Find the possible rational zeros of f(x) = x3 - 7x – 6 = 0.• p: 1, 2, 3, 6• q: 1• p/q: 1, 2, 3, 6

How do we know which zeros will work?!•Solve x3 - 7x – 6 = 0.

▫p/q: 1, 2, 3, 6

•Factor Theorem• Evaluate the function at the possible

rational zeros

Example 7. Find all real zeros of 3x3 – 20x2 + 23x + 10.•p: 1, 2, 5, 10• q: 1, 3• p/q: 1, 2, 5, 10, 1/3, 2/3, 5/3, 10/3One zero is 2. Two more come from solving using

synthetic division 3x2 14x 50

3x 1 x 5 0

x 50 x 5

3x 10 x 13

Example:Find the possible and real zeros of •Rational Root Test:

332)( 23 xxxg

AssignmentFind all the possible zeros of the function

25) 2x3 +3x2 + 1

26) 2x3 - 19x2 + 33x – 9

27) 9x4 - 9x3 -58x2 + 4x + 24

28) 2x4 - 15x3 + 23x2 + 15x - 25