Question

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

Answer 1

SOLUTION

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

$\begin{gathered} x^2 \\ \operatorname{mean}s\text{ x=0 occurs twice} \end{gathered}$

Then

x =0 has the multiplicity of 2

For

$\begin{gathered} (x-3)^3 \\ \operatorname{mean}s\text{ (x-3) occurs thrice} \end{gathered}$

x = 3 has a multiplicity of 3