Question

Write the polynomial in simplest form with roots 4, 5i, and -5i

Answer 1

i = sqrt(-1)
Roots 4, 5i and -5i will come out too
(x-4)(x+5i)(x-5i)

The first part will be \[x ^{2}+5i-4x-20i \] Then Combining like terms, and multiplying by the leftover (x-5i)

\[x ^{2}-15i-4x(x-5i) \rightarrow x ^{3}-x5i ^{2}-x15i+75i ^{2}-4x ^{2}+x20i\]
Combining Like terms again, and knowing that i^2 = -1

For our final Polynomial we get the cubic polynomial

\[x ^{3} -4x ^{2}+5x-75\]

Answer 2

If you have any questions, let me know @tayromo.