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)

Read more on -

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.