Answer:
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
