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.
Accepted Solution
A:
Answer:AStep-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=0x=-4 x=1 x=2 x=4First 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 integersIntegers are real numbers.So A.