Answer:
2x² -15x +26 = 0
Step-by-step explanation:
You want the quadratic with roots α+2 and β+2, given the roots of 2x² -7x +4 = 0 are α and β.
Monic polynomial
Dividing by the leading coefficient, the polynomial becomes ...
x² -7/2x +2 = 0
If the roots are α and β, the factored form of the polynomial is ...
(x -α)(x -β) = x² -(α+β)x +αβ
That is, α+β = 7/2, and αβ = 2.
Adding 2 to each of the roots gives ...
(x -(α+2))(x -(β+2)) = x² -(α+β+4)x +(αβ +2(α+β) +4)
Using the above values for α+β and αβ, this becomes ...
= x² -(7/2+4)x +(2+2(7/2)+4)
= x² -(15/2)x +13
Eliminating fractions, our revised quadratic is ...
2x² -15x +26 = 0
