<PRE><B>Question 672198</B>
Find all the zeros of each equation
x^5 – 3x^4 – 15x^3 + 45x^2 – 16x + 48 = 0
And the awnsers it can be are:
A: 3, 4, i
B: 4, –4, i,–i
C: 3, 4, –4, i, –i
D: 3, –4, –i 
.
Use synthetic division...
.
x^5 – 3x^4 – 15x^3 + 45x^2 – 16x + 48 = 0
Testing 3 as a solution...
3  | 1  -3  -15   45  -16  48
         3    0  -45    0 -48
    -------------------------------
     1   0  -15    0  -16   0
.
x^4 + 0x^3 - 15x^2 + 0x -16
Testing 4 as a solution...
.
4  | 1  0  -15   0  -16
        4   16   4   16
    -------------------------------
     1  4    1   4    0
.
x^3 + 4x + x + 4
.
Testing -4 as a solution...
-4  | 1  4   1   4
        -4   0  -4
     ------------------
      1  0   1   0
.
x^2 + 1
set to zero:
x^2 + 1 = 0
x^2 = -1
x = +-i
.
answer: c


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