Given the replacement set {0, 1, 2, 3, 4}, solve 6x – 3 = 3.
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A graph shows the function can be factored as
f(x) = (x -1)((x-8)² +1)
There is one real root and there are two complex roots. The latter can be found from the vertex form factor:
(x - 8)² + 1 = 0
(x - 8)² = -1
x - 8 = ±√(-1) = ±i
x = 8 ± i
The zeros of the function are {1, 8-i, 8+i}.
f(x) = (x -1)((x-8)² +1)
There is one real root and there are two complex roots. The latter can be found from the vertex form factor:
(x - 8)² + 1 = 0
(x - 8)² = -1
x - 8 = ±√(-1) = ±i
x = 8 ± i
The zeros of the function are {1, 8-i, 8+i}.