PLEASE ANSWER ALL For the graph of fOx 2x xdetermine the x a

*****PLEASE ANSWER ALL******

For the graph of fOx) 2x +xdetermine the x along with their multiplicities A. x-int: 2 with multiplicity: 1, x-int: 1 with multiplicity: 1, x-int: -1 with multiplicity:1 B. x-int: -1 with multiplicity: 2, x-int: 1 with multiplicity: 1 C. x-int: 0 with multiplicity: 1, x-int: 2 with multiplicity: 1, x-int 3 with multiplicity: 1 D. x-int: -1 with multiplicity: 2, x-int: 0 with multiplicity: 1

Solution

f(x)=x³+2x²+x

f(x)=x(x²+2x+1)

f(x)= x(x+1)²

To find the x value,we need to set f(x) to zero

x(x+1)²=0

x=0      (x+1)²=0

x=0         x=-1   with a multiplicity of 2

Correct option is D

In remainder theorem,the remainder represents the value that we get on plugging c for x in f(x)