Q:

Find the roots of the polynomial equation.

Accepted Solution

A:
Answer:3 ± i5Step-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    0Since 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                                   2So the correct answer is the last one of the four given possible answers:3 ± i5