3.10 – Rational Root Theorem
How can we find the zeros of the following polynomial?
2
19
20
Rational Root Theorem
Rational Root Theorem
To determine all possible roots (zeros) of polynomial
can use the rational root theorem.
⋯
, you
The rational root theorem is when you take all possible factors (both positive and negative
versions) of the constant p and divide them by all possible factors of the leading coefficient q.
Rational Root Theorem
List all the possible roots of the following polynomials. Do not find the zeros.
2
5
16
4
3
10
10
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial.
2
19
20
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial.
19
30
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial.
2
17
45
36
(4, 3, 3/2)
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial.
6
23
5
4
(4, two irrational roots)
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial.
!
2
13
14
24
(1, -2, 3, -4)
Rational Root Theorem
Use the Rational Root Theorem to find all of the zeros. Then, sketch a rough graph of
each polynomial. Let’s use a calculator on this one ☺
12
20
3
5
3.10 – Homework
3.10 Worksheet