One zero of f(x) = x3 – 6x2 + 11x – 6 is 3. What are other zeros of the function?
answer is 1 and 2
show work
To find the other zeros of the function, we can use polynomial long division or synthetic division. Using synthetic division:
x3 - 6x2 + 11x - 6 divided by (x - 3):
3 | 1 -6 11 -6
| 3 -9 6
------------------
1 -3 2 0
The resulting polynomial is 1x^2 - 3x + 2 (quotient) with a remainder of 0.
The zero of the resulting polynomial is the remaining factor, which can be factored as (x - 1)(x - 2).
Setting this factor equal to zero, we can find the other zeros:
x - 1 = 0 --> x = 1
x - 2 = 0 --> x = 2
Therefore, the other zeros of the function f(x) = x^3 - 6x^2 + 11x - 6 are 1 and 2.