Question

Find all the zeros for the following function.

x^3-3x^2+16x-48
there has to be a number with an i

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the zeros of a function, we need to set the function equal to zero and solve for x.

x^3 - 3x^2 + 16x - 48 = 0

Unfortunately, there is no simple method to find the zeros of a polynomial of degree 3 (cubic function). Therefore, we will need to use a numerical method or try to find rational roots.

One possible rational root is ±1, since the factors of 48 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.

Let's test x = 1:
(1)^3 - 3(1)^2 + 16(1) - 48 = 1 - 3 + 16 - 48 = -34
Since -34 is not zero, x = 1 is not a zero.

Let's test x = -1:
(-1)^3 - 3(-1)^2 + 16(-1) - 48 = -1 - 3 - 16 - 48 = -68
Since -68 is not zero, x = -1 is not a zero.

Now, we can try factoring the polynomial or use numerical methods to find the zeros.