To find your equation, simply work the problem backwards:

Let:

x = 2 and x = 4

x - 2 = 0 and x - 4 = 0

(x - 2)(x - 4) = 0

From here use FOIL:

`x^2 - 6x + 8 = 0`

` `

The term "simplest" in the question refers to finding an equation that only has 4 and 2 as its roots and there are no common factors in the coefficients of the terms of the equation. A quadratic equation has only 2 solutions.

If the roots are a and b, the quadratic equation is of the form x^2 - (a + b)*x + a*b = 0.

For roots 4 and 2, the simplest quadratic equation is x^2 - 6x + 8 = 0.

**The required equation with roots 4 and 2 is x^2 - 6x + 8 = 0.**