Question

Find the coefficients of the polynomial with a leading coefficient of: one, and roots: zero, nine, and nine.

x^3+__x^2 +81x+__

Answer 1

`zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill`