Find the roots of the polynomial equation.

3 ± i5

Step-by-step explanation:

Here we're given four sets of possible roots of the given polynomial.   Each set consists of two complex quantities and 1 real quantity.

First, we determine whether +4 is a root, then whether -4 is a root.  Let's use synthetic division to do that:

4   /  1   -2    10   136

             4      8    72

        1     2    18    208     Since the remainder is not zero, 4 is not a root.

Eliminate the first two possible answer choices, and assume that -4 is a root.

Let's check this out to be certain:

-4  /  1   -2    10   136

             -4   24  -136

        1     -6    34    0

Since the rem. is zero, -4 is a root, and the coefficients of the 2nd-degree quotient are 1, -6 and 34.

In other words, a = 1, b = -6 and c = 34.

Let's apply the quadratic rule to find the roots:

       6 ± √(36 - 4[1][34] )       6 ± √ (-100)

x = = = 3 ± i5

                     2                                   2

So the correct answer is the last one of the four given possible answers:

3 ± i5

x=30

step-by-step explanation: