Question

write a polynomial function for f(2)=0 with a multiplicity of 2 and f(-1)=0

Answer 1

We have the following:

Being a multiplicity of two, then we only have to multiply two factors

We must create a polynomial that, like 0, its solution is 2 and that is -1, in the following way

$\begin{gathered} x=2\Rightarrow x-2=0 \\ x=-1\Rightarrow x+1=0 \\ \text{ we multiply the factors} \\ (x-2)\cdot(x+1)=0 \\ x^2+x-2x-2=0 \\ x^2-x-2=0 \end{gathered}$

Therefore, the answer is the option d.

$f(x)=x^2-x-2$