Review SYNTHETIC DIVISION

1
Review SYNTHETIC DIVISION to find roots of
third degree characteristic polynomial
Pamela Leutwyler
2
(2x 5)(x 3)(7x 2)
3
(2x 5)(x 3)(7x 2) 14x3 3x2 107x
30 0
4
The roots are
-3
(2x 5)(x 3)(7x 2) 14x3 3x2 107x
30 0
5
The roots are
-3
(2x 5)(1x 3)(7x 2) 14x3 3x2 107x
30 0
6
The roots are
-3
(2x 5)(1x 3)(7x 2) 14x3 3x2 107x
30 0
7
The roots are
-3
(2x 5)(1x 3)(7x 2) 14x3 3x2 107x
30 0
If
is a root of the polynomial equation
8
The roots are
-3
2
7
1
(2x 5)(1x 3)(7x 2) 14x3 3x2 107x
30 0
If
is a root of the polynomial equation
Then q is a factor of 14
9
5
2
The roots are
-3
-3
2
7
1
(2x 5)(1x 3)(7x 2) 14x3 3x2 107x
30 0
If
is a root of the polynomial equation
Then q is a factor of 14 and p is a factor of
30
10
A characteristic polynomial will always have lead
coefficient 1. Rational eigenvalues will be
integral factors of the constant coefficient of
the characteristic polynomial .
example find the eigenvalues for the matrix
11
potential rational roots are factors of 14.
1, -1, 2, -2, 7, -7, 14, -14
Test the potrats using synthetic division
? 1 -4 -19 -14
12
potential rational roots are factors of 14.
1, -1, 2, -2, 7, -7, 14, -14
Test the potrats using synthetic division
1? 1 -4 -19 -14
-3
-22
1
-36
-22
1
-3
13
potential rational roots are factors of 14.
1, -1, 2, -2, 7, -7, 14, -14
Test the potrats using synthetic division
7? 1 -4 -19 -14
21
14
7
0
2
1
3
14
potential rational roots are factors of 14.
1, -1, 2, -2, 7, -7, 14, -14
Test the potrats using synthetic division
7? 1 -4 -19 -14
21
14
7
0
2
1
3
factor this or use quadratic formula or continue
with synthetic division to get the other roots.