Question

What is the value of z so that -9 and 9 are both solutipns fo x^2+z=103

Answer 1

well, we know the solutions are -9 and 9, so, let's just FOIL them then


`\bf \begin{cases} x=-9\implies &x+9=0\\ x=9\implies &x-9=0 \end{cases} \\\\\\ (x+9)(x-9)=\stackrel{original~polynomial}{0}\implies x^2+0x-81=0 \\\\\\ x^2\underline{-81}=0\qquad \textit{and we can write }-81=\underline{-103+22} \\\\\\ x^2\underline{-103+22}=0\implies x^2+22=103`