4. The conventional algorithm for evaluating a polynomial anx" + an-1x¹ +... + a1x + ao at x = c can be expressed in pseudocode as Algorithm Polynomial (c, ao, a₁,...,an: real numbers) power = 1; y = ao; for i = 1 to n power power * c; y = y + ai * power return y; Notice that the final value of y is y = anc" + an-1 c¹ +...+ a₁c + ao, the value of the polynomial at x = c. a) Evaluate 3x² + x +1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. b) Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)
4. The conventional algorithm for evaluating a polynomial anx" + an-1x¹ +... + a1x + ao at x = c can be expressed in pseudocode as Algorithm Polynomial (c, ao, a₁,...,an: real numbers) power = 1; y = ao; for i = 1 to n power power * c; y = y + ai * power return y; Notice that the final value of y is y = anc" + an-1 c¹ +...+ a₁c + ao, the value of the polynomial at x = c. a) Evaluate 3x² + x +1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. b) Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. The conventional algorithm for evaluating a polynomial anx" + an-1x¹ +... + a1x + ao at x = c can be
expressed in pseudocode as
Algorithm Polynomial (c, ao, a₁,...,an: real numbers)
power = 1;
y = ao;
for i = 1 to n
power power * c;
y = y + ai * power
return y;
Notice that the final value of y is y = anc" + an-1 c¹ +...+ a₁c + ao, the value of the polynomial
at x = c.
a) Evaluate 3x² + x +1 at x = 2 by working through each step of the algorithm showing the values
assigned at each assignment step.
b) Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at
x = c? (Do not count additions used to increment the loop variable.)
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