Polynomial/f(-1) is 2,f(1) is 0,f(3) is 5/System/Exercise/Solution

The conditions lead to the system of linear equations

${}a-b+c=2\,,$

${}a+b+c=0\,,$

${}a+3b+9c=5\,.$

${}I-II$ yields

${}b=-1\,$

and ${}I-III$ yields

${}-4b-8c=-3\,,$

hence

${}c={\frac {3}{8}}-{\frac {1}{2}}b={\frac {3}{8}}+{\frac {1}{2}}={\frac {7}{8}}\,$

and so

${}a={\frac {1}{8}}\,.$

The looked-for polynomial is therefore

${\frac {1}{8}}-X+{\frac {7}{8}}X^{2}.$

To the exercise