Given:
The function is
[tex]f(x)=(x+3)^2(x-5)^6[/tex]
To find:
The zeros of the given function.
Solution:
The general form of polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex] ...(i)
where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeros of respective multiplicities [tex]m_1,m_2,...,m_n[/tex].
We have,
[tex]f(x)=(x+3)^2(x-5)^6[/tex]
On comparing this with (i), we get
[tex]c_1=-3,m_1=2[/tex]
[tex]c_2=5,m_2=6[/tex]
It means, -3 is a zero with multiplicity 2 and 5 is a zero with multiplicity 6.
Therefore, the correct option is B.
