1. 4.2 Real Zeros
Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0.
Zero, solution, root x-intercepts

2. Rational Zeros: zeros that are rational #’s
The Rational Zero Test
All possible rational zeros can be determined by where
r is the factors of the constant
s is the factors of the coefficient

3. Ex.1 a)Find all possible rational zeros of f(x) = 2x4 + x3 -17x2 – 4x + 6 r = s = b) Determine the rational zeros.

4. Ex. 2 Find all REAL zeros of f(x) = 2x4 + x3 - 17x2 – 4x + 6

5. Bounds Test: Used to determine which #’s ALL zeros are between
Upper bound – a #  0 that results in the last row in synthetic division being nonnegative.
Lower bound – a #  0 that results in the last row in synthetic division alternating positive and negative.

6. Ex. 3 Find all real zeros of f(x) = x6 + x3 – 7x2 - 3x + 1 a) Find all rational zeros. r = s = b) Use the bounds test to find lower & upper bounds for the zeros. c) Use calculator to approximate the zeros.

7. Ex. 4 Find all real zeros of f(x) = x7 – 6x6 + 9x5 + 7x4 – 28x3 + 33x2 - 36x + 20