Find multiplicity of the polynomial
$f (x) = (x - 1)^{2} (2 x + 5)^{3} (x^{2} + 1)^{2} (x + π^{2})^{4}$

4

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2

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8

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1

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Solution

The correct option is A $4$
The roots of the given function are $1, - \frac{5}{2}, - i, i, - π^{2}$
The multiplicity of $x = 1$ is $2$
The multiplicity of $x = - \frac{5}{2}$ is $3$
The multiplicity of $x = i$ is $2$
The multiplicity of $x = - i$ is $2$
The multiplicity of $x = - π^{2}$ is $4$
Therefore the multiplicity of polynomial is $4$
Therefor option $A$ is correct

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