How do you find all the zeros of #F (x) = 5x^3 (x+ 3)^ 4 (x7)# with all its multiplicities?
1 Answer
Aug 20, 2017
The zeros are:
#x=0" "# with multiplicity#3#
#x=3" "# with multiplicity#4#
#x=7" "# with multiplicity#1#
Explanation:

Each linear factor corresponds to a zero. That is:
#a# is a zero if and only if#(xa)# is a factor. 
The multiplicity of each factor is the multiplicity of the corresponding zero.
We can rewrite the given
#5x^3(x+3)^4(x7) = 5(x0)^3(x(3))^4(x7)#
So the zeros are:
#x=0" "# with multiplicity#3#
#x=3" "# with multiplicity#4#
#x=7" "# with multiplicity#1#