Verified answer

Not quite; you've left out some parentheses in your typing.

Given those roots, you know that the equation is of the form

a (x - (2+√3)) (x - (2-√3))

Now we multiply the two x terms:

a (x^2 - (2-√3)x - (2+√3)x + (4-3)) -- note the 4-3 at the end is from the difference of squares.

a (x^2 - 2x + √3x - 2x - √3x + 1)

a(x^2 - 4x + 1)

Now, you simply need to pick the proper value for a such that (2, 5) is a solution.