Question

Form a polynomial whose zeros and degree are given. ​Zeros: negative 4​, multiplicity​ 1; negative 3​, multiplicity​ 2; degree 3

Answer 1

Answer:

Required polynomial is

$P(x)=a(x+4)(x+3)^2$

where, a can be any real number.

Step-by-step explanation:

The factored form of a polynomial is

$P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}$

where, a is constant, $c_1,c_2,...c_n$ are zeroes with multiplicity $m_1,m_2,...,m_n$ respectively.

It is given that -4 is a zero of required polynomial with multiplicity​ 1. It means $(x+4)^1$ is a factor of required polynomial.

It is given that -3 is a zero of required polynomial with multiplicity​ 2. It means $(x+3)^2$ is a factor of required polynomial.

Required polynomial is

$P(x)=a(x+4)(x+3)^2$

where, a can be any real number.