Match the polynomial to the correct description :

(X+4)(x-1)(x-2)(x-4)

A. The related polynomial equation has a total of four roots;all four roots are real.

B. the related polynomial equation has a total of four roots,all four roots are real and one root has a multiplicity of 2.

C. The related polynomial equation has a total of four roots, two roots are complex and two roots are real.

D. The related polynomial equation has a total of two roots, both roots are real and have a multiplicity of 2.

E. The related polynomial equation has a total of three roots, two roots are complex and one root is real.

F. The related polynomial equation has a total of four roots, two roots are complex and one root is real with a. Multiplicity of 2.

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freckledspots freckledspots · Answer 1 · 2019-07-05T18:58:33+02:00

Answer:

A

Step-by-step explanation:

The polynomial (x+4)(x-1)(x-2)(x-4) has zeros at x=-4,1,2,4.

The related polynomial equation is (x+4)(x-1)(x-2)(x-4)=0.

In order for this equation to be true at least one of the factors must by 0 that is the only way a product can be zero (if one of it's factors is).

So you wind up needing to solve these 4 equations:

x+4=0 x-1=0 x-2=0 x-4=0

x=-4 x=1 x=2 x=4

First equation, I subtracted 4 on both sides.

Second equation, I added 1 on both sides.

Third equation, I added 2 on both sides.

Fourth equation, I added 4 on both sides.

-4,1,2,4 are all integers

Integers are real numbers.

So A.