What is the simplest equation that has roots 4 and 2?
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.
To find your equation, simply work the problem backwards:
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`