MATH SOLVE

2 months ago

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