Step 1
Vieta's formula
[tex]\begin{gathered} ax^2+bx+c=0 \\ x_1+x_2=-\frac{b}{a} \\ x_1\cdot x_2=\frac{c}{a} \end{gathered}[/tex]
Step 2
Let
[tex]ax^2+bx+c=0=-z^2+z[/tex]
then
[tex]\begin{gathered} a=-1 \\ b=1 \\ c=0 \end{gathered}[/tex]
Step 3
replace
[tex]\begin{gathered} x_1+x_2=\frac{-(1)}{-1} \\ z_1+z_2=1 \end{gathered}[/tex]
and
[tex]\begin{gathered} z_1\cdot z_2=\frac{0}{-1} \\ z_1\cdot z_2=0 \end{gathered}[/tex]
so, the answers are 1 and 0
