Plz plz
match each polynomial with the appropriate explanation regarding the roots of the related polynomial equation.

(a) (x+4)(x−4)[x−(2−i)][x−(2+i)]
(b) (x+i)(x−i)(x−2)3(x−4)
(c) (x+3)(x−5)(x+2)^2
(d) (x+2)2(x+1)^2

(1) the related polynomial equation has a total of four roots; all four roots are real and one root has a multiplicity of 2 .
(2) the related polynomial equation has a total four roots; all four roots are real and two roots have a multiplicity of 2 .
(3) the related polynomial equation has a total of two real roots; both roots are real and have a multiplicity of 2 .
(4) the related polynomial equation has a total of six roots; two roots are complex and the one of the remaining real roots has a multiplicity of 3 .
(5) the related polynomial equation has a total of four roots; two roots are complex and two roots are real.
(6) the related polynomial equation has a total of three roots; all three roots are real and one root has a multiplicity of 2 .

(A) - (5)

(B) - (4)

(C) - (1)

(D) - (2)

Step-by-step explanation:

(A) We are given the polynomial (x+4)(x−4)[x−(2−i)][x−(2+i)]

(5) The related polynomial equation has a total of four roots; two roots are complex and two roots are real.

(B) We are given the polynomial (x+i)(x−i)(x−2)³(x−4).

(4) The related polynomial equation has a total of six roots; two roots are complex and one of the remaining real roots has a multiplicity of 3.

(C) We are given the polynomial (x+3)(x−5)(x+2)²

(1) The related polynomial equation has a total of four roots; all four roots are real and one root has a multiplicity of 2.

(D) We are given the polynomial (x+2)²(x+1)²

(2)  The related polynomial equation has a total four roots; all four roots are real and two roots have a multiplicity of 2. (Answer)

step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)