Determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4. 0 has multiplicity −2 has multiplicity −4 has multiplicity 5 has multiplicity

Answer:0 has multiplicity 1-2 has multiplicity 3-4 has multiplicity 25 has multiplicity 4Step-by-step explanation:The multiplicity of the root of a polynomial function, refers to the number of time the root repeats itself.The given function is [tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]To find the roots of this function, we equate the function to zero.[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]We now use the zero product principle, to obtain;[tex]x=0[/tex], with multiplicity 1[tex](x+2)^3=0[/tex][tex]\Rightarrow x=-2[/tex], with multiplicity 3[tex](x+4)^2=0[/tex][tex]\Rightarrow x=-4[/tex], with multiplicity 2[tex](x-5)^4=0[/tex][tex]\Rightarrow x=5[/tex], with multiplicity 5.