Question

Write a polynomial of the smallest degree with roots 4i and -4i.

Answer 1

if \(r\) is a root of a polynomial then \(x-r\) is a factor of the polynomial.

here the roots are \(4i\) and \(4i\), and the corresponding factors are \(x-4i\) and \(x+4i\)

your polynomial is \(f(x) = (x-4i)(x+4i)\). just expand...

Answer 2

correction. the roots are \(4i\) and \(-4i\).

the rest remains the same.

Answer 3

ok thank you for the help

Answer 4

yw.