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:

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d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.