Question

Find a cubic function with the given zeros. Square root of five., - Square root of five., -7

Answer 1

`\bf x= \begin{cases} \pm √(5)\\ -7 \end{cases}\implies \begin{cases} x=√(5)\implies &(x-√(5))=0\\ x=-√(5)\implies &(x+√(5))=0\\ x=-7\implies &(x+7)=0 \end{cases} \\\\\\ \stackrel{\textit{difference of squares}}{(x-√(5))(x+√(5))}(x+7)=\textit{original polynomial} \\\\\\ (x^2-5)(x+7)=y\implies x^3+7x^2-5x-35=y`