Question

write a least degree polynomial whose zeros are 5i and -4

Answer 1

3rd degree

Answer 2

5i is a complex conjugate so therefore -5i is also a solution

Answer 3

\[x = \pm 5i\]
\[x^2 = -25\]
\[x^2 + 25 = 0\]
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\[x = -4\]
\[x +4 = 0\]

Now we have factored form of polynomial
\[(x^2 +25)(x+4)\]
distribute to get standard form
\[x^3 + 4x^2 +25x+100\]