Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.3 Applications of Systems of Linear Equations - 1.3 Exercises - Page 32: 1

Answer

$$ p(x)=29-18 x+3 x^{2}. $$

Work Step by Step

Suppose that $$ p(x)=a_{0}+a_{1} x+a_{2} x^{2}. $$ Now, we have $$ \begin{array}{l}{p(2)=a_{0}+a_{1}(2)+a_{2}(2)^{2}=a_{0}+2a_{1}+4a_{2}=5} \\ {p(3)=a_{0}+a_{1}(3)+a_{2}(3)^{2}=a_{0}+3 a_{1}+9 a_{2}=2} \\ {p(4)=a_{0}+a_{1}(4)+a_{2}(4)^{2}=a_{0}+4 a_{1}+16 a_{2}=5} \end{array} $$ The above system gas the solution $$a_{0}=29, \quad a_{1}=-18, \quad a_{2}=3.$$ Hence, $$ p(x)=29-18 x+3 x^{2}. $$
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