Final answer:
To find the real roots of the equation and determine the values of A and B, we use the fact that 1 + i is one of the roots. We set up an equation using the sum of the roots and solve for the real root. From there, we can calculate the values of A and B.
Step-by-step explanation:
In order to find the real roots of the equation and determine the values of A and B, we can use the fact that 1 + i is one of the roots of the equation. Since complex roots come in conjugate pairs, the other two roots must be 1 - i and a real number.
We know that the sum of the roots of a cubic equation is equal to the opposite of the coefficient of the quadratic term. In this case, the sum of the roots is (1 + i) + (1 - i) + r, where r is the real root. This sum must equal -A.
Using this information, we can set up the equation (1 + i) + (1 - i) + r = -A and solve for r. Once we find r, we can find the values of A and B by considering the product and sum of the roots.