Answer:
The multiple zero is [tex]x=-5[/tex].
The multiplicity is 2
Step-by-step explanation:
The given function is
[tex]f(x)=x^3+10x^2+25x[/tex]
To find the zero of this function, we equate it to zero.
[tex]\Rightarrow x^3+10x^2+25x=0[/tex]
We factor to obtain;
[tex]x(x^2+10x+25)=0[/tex]
Observe that; the expression within the parenthesis is a perfect square.
This implies that;
[tex]x(x+5)^2=0[/tex]
This implies that;
Either [tex]x=0[/tex] or [tex](x+5)^2=0[/tex]
[tex](x+5)^2=0[/tex] has a multiple zero which is
[tex]x=-5[/tex] and its multplicity is 2.
