Question

Y = x²(x – 3)³ find the zeros of each function, state the multiplicity of multiple zeros

Answer 1

Write out the equation given

`y=x^2(x-3)^3`

The zeros of the polynomial is obtain by equating the polynomial to zero.

Hence

`x^2(x-3)^3=0`

Equate each product to zero, we have

`\begin{gathered} x=0\text{ or x-3=0} \\ x=0,\text{ x=3} \end{gathered}`

The zeros of the polynomial are

`0,\text{ and 3}`

The zeros of the polynomials is 0 and 3

the multiplicity of multiple zeros​ is the number of times the zeros of the polynomial occur which is obtain from the degree of each terms in the polynomial.

Hence

Then

x =0 has the multiplicity of 2

For

x = 3 has a multiplicity of 3