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aivan3 [116]
3 years ago
5

Find the zeros of the polynomial function: f(x) = 9x^3 - 27x^2 - 4x + 12.

Mathematics
1 answer:
hichkok12 [17]3 years ago
3 0

Answer:

  {-2/3, 2/3, 3}

Step-by-step explanation:

The equation can be factored by grouping.

  f(x) = (9x^3 -27x^2) +(-4x +12)

  f(x) = 9x^2(x -3) -4(x -3)

  f(x) = (9x^2 -4)(x -3)

We recognize the first factor as the difference of squares, so know it can be further factored to give ...

  f(x) = (3x -2)(3x +2)(x -3)

The zeros are the values of x that make these factors be zero:

  3x -2 = 0   ⇒   x = 2/3

  3x +2 = 0   ⇒   x = -2/3

  x -3 = 0   ⇒   x = 3

The zeros of the polynomial are x = -2/3, 2/3, 3.

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