Page 16 - Numerical Analysis Using MATLAB and Excel

Roots of Polynomials

displays

z =
3.0000 - 4.0000i
4
In the example above, a multiplication (*) sign between and was not necessary because the
j
complex number consists of numerical constants. However, if the imaginary part is a function or
variable such as cos x () , we must use the multiplication sign, that is, we must type cos(x)*j or
j*cos(x).

1.2 Roots of Polynomials

[
In MATLAB, a polynomial is expressed as a row vector of the form a a n – 1 a a a ] 2 1 0 . The
n
a
elements of this vector are the coefficients of the polynomial in descending order. We must
i
include terms whose coefficients are zero.
We can find the roots of any polynomial with the roots(p) function where p is a row vector con-
taining the polynomial coefficients in descending order.

Example 1.1
Find the roots of the polynomial

3
4
2
p x() = x – 10x + 35x – 50x + 24 (1.1)
1
Solution:
The roots are found with the following two statements. We have denoted the polynomial as p1,
and the roots as roots_ p1.

p1=[1 −10 35 −50 24] % Specify the coefficients of p1(x)

p1 =
1 -10 35 -50 24
roots_ p1=roots(p1) % Find the roots of p1(x)

roots_p1 =
4.0000
3.0000
2.0000
1.0000
We observe that MATLAB displays the polynomial coefficients as a row vector, and the roots as a
column vector.

Numerical Analysis Using MATLAB® and Excel®, Third Edition 1−3
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