Roots:
Say the roots of a quadratic equation are m and n, x=m and x=n.
The equation will be
[tex](x-m)(x-n)=0 \\ x^2-mx-nx+mn=0 \\ \boxed{x^2-(m+n)x+mn=0}[/tex]
Recall the form of a quadratic equation: [tex]ax^2+bx+c=0[/tex]
In the derived equation from the example above, you will notice that b in the bx term is equal to the negative sum of the roots, and the constant c is equal to the product of the roots.
To summarize, a quadratic equation may be derived by using the following pattern:
[tex] x^{2} -[sum]x+[product]=0[/tex]
