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Explanation:
The given zeros are: 4, -8, 2+3i
All coefficients are real numbers, so this means that the root 2+3i must be paired with 2-3i which is its conjugate pair.
While we are given 3 roots, there are actually four roots and they are: 4, -8, 2+3i, 2-3i
This means,
x = 4 or x = -8 or x = 2+3i or x=2-3i
x-4=0 or x+8=0 or x-2=3i or x-2=-3i
x-4=0 or x+8=0 or (x-2)^2=(3i)^2 or (x-2)^2=(-3i)^2
x-4=0 or x+8=0 or (x-2)^2=-9 or (x-2)^2=-9
x-4=0 or x+8=0 or (x-2)^2=-9
x-4=0 or x+8=0 or (x-2)^2+9=0
(x-4)(x+8)((x-2)^2+9)=0
(x-4)(x+8)(x^2-4x+4+9)=0
(x-4)(x+8)(x^2-4x+13)=0
(x^2+4x-32)(x^2-4x+13)=0
x^4-35x^2+180x-416 = 0 .... see attached image below
If you work your way backwards up the steps listed here, then you'll go from x^4-35x^2+180x-416 = 0 to x = 4 or x = -8 or x = 2+3i or x=2-3i
This shows f(x) = x^4-35x^2+180x-416 has the four roots x = 4, x = -8, x = 2+3i, x = 2-3i
First we need to know how many months is 2 years. To answer that we multiply the number of months in a year by 2 and get 48 months.
Every 3 months the population of turtles doubles, but to get how many times the population doubles, you need to divide 48 months by 3 to get 16.
So population of 400 will get <u>doubled</u> 16 times in the following <u>two</u> years.
We construct the following equation where is the final population,
Hope this helps. :)