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

User Glm
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1 Answer

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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.

User Thomson Ignesious
by
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