Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2) f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

D is correct

Step-by-step explanation:

We are given roots and leading coefficient of any polynomial.

Roots are -4,i and 2.

All are multiplicity 1.

One root is complex. As we know complex root in conjugate pair.

So, Conjugate of "i" is "-i"

Now, we have four roots with multiplicity 1

Required polynomial:

where, a is leading coefficient

So, a=3

Hence, The required polynomial function is

Step-by-step explanation:

For this case we have the following function:

f (x) = (x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9)

The leading coefficient is the coefficient that accompanies the variable with the highest degree of the polynomial.

Applying the distributive property, it can be seen that this coefficient is equal to 1.

The roots of the polynomial are given by:

(x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9) = 0

Solution 1:

x + 5 = 0

x = -5 (multiplicity equal to 3)

Solution 2:

x + 4 = 0

x = -4 (multiplicity equal to 1)

Solution 3:

x-2 = 0

x = 2 (multiplicity equal to 1)

Solution 4:

x-9 = 0

x = 9 (multiplicity equal to 1)

option 3

f (x) = (x + 5) (x + 5) (x + 5) (x + 4) (x - 2) (x - 9)

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what is all that apply?

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.