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: 4


$$ p(x)=4. $$

Work Step by Step

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