107k views
4 votes
Find the zeros of the polynomial
function and state the multiplicity of
each

Find the zeros of the polynomial function and state the multiplicity of each-example-1

2 Answers

1 vote
Hi the answer zero ther u go
User Pawel Miech
by
7.7k points
5 votes

The zeros of the polynomial function
y=5(x-4) ^2 (x-6) ^3and their multiplicities are:

4 with multiplicity 2

6 with multiplicity 3

The multiplicity of a zero is the number of times it appears in the factored form of the polynomial. In this case, the factor (x−4) appears twice, so the zero at x=4 has multiplicity 2. The factor (x−6) appears three times, so the zero at x=6 has multiplicity 3.

To find the zeros of a polynomial, we can set the polynomial equal to zero and solve the resulting equation. In this case, we have:


5(x-4)^2(x-6)^3 = 0

This equation is true if any of the factors is equal to zero. So, we have three equations to solve:

x-4 = 0

x-6 = 0

x-6 = 0

The first equation has the solution x=4. The second equation has the solution x=6. The third equation has the solution x=6.

Therefore, the zeros of the polynomial are x=4 and x=6. The zero at x=4 has multiplicity 2 and the zero at x=6 has multiplicity 3.

User AlliceSmash
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories