Solution:
The quadratic expression is given below as
[tex]x^2-x-56[/tex]
Using the smiley method below , we will have it represents as
Let the two factors be represented below as
[tex]m,n[/tex]
The product of the two factors will give us
[tex]mn=-56-----(1)[/tex]
The sum of the two factors, will give
[tex]\begin{gathered} m+n=-1----(2) \\ \end{gathered}[/tex]
from equation (2) make m the subject of the formula
[tex]\begin{gathered} m+n=-1 \\ m=-1-n-----(3) \end{gathered}[/tex]
Substitute equation 3 in equation (1)
[tex]\begin{gathered} mn=-56 \\ n(-1-n)=-56 \\ -n-n^2=-56 \\ -n^2-n=-56 \\ -n^2-n+56=0 \\ -n^2-8n+7n+56=0 \\ -n(n+8)+7(n+8)=0 \\ (7-n)(n+8)=0 \\ 7-n=0,n+8=0 \\ n=7,n=-8 \end{gathered}[/tex]
Substitute n=7 and n=-8 in equation (3)
[tex]\begin{gathered} m=-1-n,when\text{ }n=7 \\ m=-1-7 \\ m=-8 \\ n=-1-n,whenn=-8 \\ m=-1-(-8) \\ m=-1+8=7 \end{gathered}[/tex]
Hence,
The final answers are
[tex]\begin{gathered} \Rightarrow mn=-56 \\ \Rightarrow m+n=-1 \\ \Rightarrow m=7,n=-8 \\ \Rightarrow m=-8,n=7 \end{gathered}[/tex]
