Question

Write a polynomial with zeros at x= 1,9,3.5

Answer 1

`\begin{cases} x = 1 &\implies x -1=0\\ x = 9 &\implies x -9=0\\ x = 3 &\implies x -3=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -1 )( x -9 )( x -3 )( x -5 ) = \stackrel{0}{y}}\implies \stackrel{\textit{assuming a = 1}}{1( x -1 )( x -9 )( x -3 )( x -5 ) =y} \\\\\\ ~\hfill~ {\Large \begin{array}{llll} x^4-18x^3+104x^2-222x+135=y \end{array}} ~\hfill~`

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