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Answer:
x² -4x +1 = 0
Explanation:
For roots p and q, the factored form of the equation is ...
(x -p)(x -q) = 0
The expanded form of this is ...
x² -(p+q)x +pq = 0
So, we can find the coefficients of the quadratic by finding the sum and product of the factors.
-b = (2 -√3) + 1/(2 -√3) = (2 -√3) +(2 +√3)/((2-√3)(2+√3)) = 4
c = (2 -√3)/(2 -√3) = 1
So, the quadratic is ...
x² -4x +1 = 0