A quadratic equation can be formed by its solutions. For example, if 2 and 3 are the solutions of an unknown quadratic equation, the quadratic equation can be formed as follows:

Sum of zeros, S = 2 + 3 = 5

Product of zeros, P = 2 * 3 = 6

Substitute the value of S and P in the following equation:

x^2 - Sx + P = 0

x^2 - 5x + 6 = 0

The quadratic equation

x^2 - 5x + 6 = 0 has the two zeros, 2 and 3. You should check the solutions of the quadratic equation to ensure that you have got the correct equation. In order to do so, either apply the quadratic formula,

x = [ -(-5) +/- sqrt((-5)^2 - 4(1)(6)) ] / [ 2(1) ]

x = [ +5 +/- sqrt(25 - 24) ] [ 2 ]

x = [ 5 +/- 1 ] / 2

x = (5 + 1)/2 or x = (5 - 1)/2

x = 3 or x = 2, thus the zeros are correct.

or solve the quadratic equation by factoring it (if possible),

x^2 - 5x + 6 = 0

x^2 - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

(x - 2)(x - 3) = 0

Either x - 2 = 0 or x - 3 = 0

x = 2 or x = 3, which are the original zeros.