Question

Find a polynomial f (x) of degree 4 that has the following zeros.-1 (multiplicity 2), 3, OLeave your answer in factored form.f(x) = 0

Answer 1

The following parameters are given in the question

The zeros of the polynomial of degree 4 are given below as

`\begin{gathered} -1(m\mu\text{ltiplicity of 2)} \\ it\text{ means that,} \\ x=-1 \\ (x+1) \\ \text{having a multiplicity of 2 will make it} \\ (x+1)^2 \end{gathered}`

The other zeros given are

`\begin{gathered} x=3 \\ (x-3)\text{ and } \\ x=0 \\ \end{gathered}`

Multiplying all the factors to get the polynomial, we will have

`\begin{gathered} f(x)=(x+1)^2(x-3)(x) \\ f(x)=(x+1)(x+1)(x-3)x \\ f(x)=x(x+1)^2(x-3) \end{gathered}`

Hence,

F(x)= x(x-3)(x+1)²