Page 18 - Numerical Analysis Using MATLAB and Excel

Evaluation of a Polynomial at Specified Values

r3=[1 2 3 4] % Specify the roots of the polynomial

r3 =
1 2 3 4

poly_r3=poly(r3) % Find the polynomial coefficients

poly_r3 =
1 -10 35 -50 24
We observe that these are the coefficients of the polynomial p x() of Example 1.1.
1

Example 1.4

,
,
,
It is known that the roots of a polynomial are 1 2 3 4 + j5and 4 j5 . Find the coeffi-
,
–
–
–
–
cients of this polynomial.
Solution:
We form a row vector, say r4 , with the given roots, and we find the polynomial coefficients with
the poly(r) function as shown below.
r4=[ −1 −2 −3 4+5j 4−5j ]

r4 =
Columns 1 through 4
-1.0000 -2.0000 -3.0000 -4.0000 + 5.0000i
Column 5
-4.0000 - 5.0000i
poly_r4=poly(r4)

poly_r4 =
1 14 100 340 499 246
Therefore, the polynomial is

3
2
4
5
p x() = x + 14x + 100x + 340x + 499x + 246 (1.3)
4

1.4 Evaluation of a Polynomial at Specified Values

The polyval(p,x) function evaluates a polynomial px() at some specified value of the indepen-

x
dent variable .

Numerical Analysis Using MATLAB® and Excel®, Third Edition 1−5
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