Question

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.

Answer 1

A

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.