Question

Write the equation for whose roots are 3,0,1,i,-i

Answer 1

Given the roots: 3,0,1,i,-i

We will write the equation for whose roots are

As we were given the roots, we can write the factors

so, we have the following factors:

`\begin{gathered} x=3\rightarrow(x-3) \\ x=0\rightarrow x \\ x=1\rightarrow(x-1) \\ x=i\rightarrow(x-i) \\ x=-i\rightarrow(x+i) \end{gathered}`

So, the equation will be:

`f(x)=x(x-1)(x-3)(x-i)(x+i)`