There are two ways you can do this
[tex] <B>Using the formula</B> [/tex]
[tex] {x}^{2} - (sum \: of \: roots)x + poduct \: of \: roots = 0[/tex]
[tex] {x}^{2} - (8+-1)x + - 1 \times 8 = 0[/tex]
[tex] {x}^{2} - 7x - 8 = 0[/tex]
[tex] <B>Working backwards</B> [/tex]
[tex]x = 8 \: or \: x = - 1[/tex]
[tex] \Rightarrow x-8=0 \: or \: x+1=0[/tex]
[tex]\Rightarrow (x-8)(x + 1)=0 [/tex]
[tex]\Rightarrow {x}^{2} + x -8x - 8 = 0[/tex]
[tex]\Rightarrow {x}^{2} - 7x - 8 = 0[/tex]
