Question 672198: 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
So can someone help me I can't figure out which one it would be.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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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