Answer:
2x^2 -x +1 = 0
Explanation:
For roots α and β, the original equation can be factored as ...
f(x) = 2(x -α)(x -β)
If we add 1 to each of those roots, the factors become ...
g(x) = 2(x -(α+1))(x -(β+1))
This can be rearranged to be ...
g(x) = 2((x -1) -α)((x -1) -β)
That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.
2(x -1)² +3(x -1) +2 = 0
2x^2 -x +1 = 0