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Say the roots of a quadratic equation are m and n, x=m and x=n.
The equation will be 
(x-m)(x-n)=0 \\ x^2-mx-nx+mn=0 \\ \boxed{x^2-(m+n)x+mn=0}

Recall the form of a quadratic equation: ax^2+bx+c=0

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:
 x^{2} -[sum]x+[product]=0