Example 3: Find the quadratic equation if we know that the roots are 2 and 3.
The general form of the quadratic equation is found by the following steps.

(1) 
Now we can add and multiply solutions (1) to get the result of x_{1} and x_{2} as a function of the coefficients a, b and c as follows.

(2)
(3) 
Substitute given solutions x_{1} = 2 and x_{2} = 3 into equations (2) and (3).
b = −(x_{1} + x_{2})a = −(2 + 3)a = −5a
c = x_{1}x_{2}a = 2 ‧ 3a = 6a
If we chose a = 1 than the quadratic equation will be: x^{2} − 5x + 6 = 0
