Let 1 + i be one of the root of z^3 + az^2 + bz + 26 = 0, then find the real roots of the equation and determine the value of a and b.

The real root is -13

The value of A is 11 and B is -24

Step-by-step explanation:

The given equation is .

If is a root then then the complex conjugate is also a root.

Let us now derive the quadratic equation that gave rise to this complex roots.

By the factor theorem, we get;

Now the  

Now the fully factored cubic polynomial will be of the form:

By comparing constant terms; 2c=26. This means c=13

Hence  the required polynomial is

Therefore the real root is z=-13

We now expand fully to get:

By comparing coefficients; A=11, and B=-24

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step-by-step explanation: