However it is dicult to see what is happening near x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the list of candidates for rational zeros you obtained in Example 3.3.2. 3. Use synthetic division to find the real zeros of f , and state their multiplicities. Solution. 1. In Example 3.3.1, we determined all of the real zeros of f lie in the interval [−4, 4]. We set our window accordingly and get 3.3 Real Zeros of Polynomials 209 2. In Example 3.3.2, we learned that any rational zero of f must be in the list ± 1 , ± 1, ± 3 , ± 3 . 2 2 From the graph, it looks as if we can rule out any of the positive rational zeros, since the graph seems to cross the x-axis at a value just a little greater than 1. On the negative side, −1 looks good, so we try that for our synthetic division. −1 2 4 −1 −6 −3 ↓ −2 −2 3 3 2 2 −3 −3 0 We have a winner! Remembering that f was a fourth degree polynomial, we now know our quotient is a third degree polynomial. If we can do one more successful division, we will have knocked the quotient down to a quadratic, and, if all else fails, we can use the quadratic formula to find the las...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online