Question

. y = x (x + 2)^2
Find the zeros of each function. State the multiplicity of multiple zeros

Answer 1

Given:

The function is
`y=x(x+2)^2`.

To find:

The zeros and their multiplicity.

Solution:

A polynomial is defined as

`y=a(x-c_1)^(m_1)(x-c_2)^(m_2)...(x-c_n)^(m_n)` ...(i)

where, a is a constant,
`c_1,c_2,...,c_n` are zeros with multiplicity
`m_1,m_2,...,m_n` respectively.

We have,

`y=x(x+2)^2`

It can be written as

`y=(x-0)^1(x-(-2))^2` ...(ii)

On comparing (i) and (ii), we get

`c_1=0,m_1=1`

`c_2=-2,m_2=2`

Therefore, the zeros of the given function are 0 and -2 with multiplicity 1 and 2 respectively.