How do you write a polynomial with zeros i, -3i, 3i and leading coefficient 1?

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Answer 1 · 2016-10-08T08:14:43

The polynomial with zeros #i#, #-3i# and #3i#

is #x^3-ix^2+9x-9i#

A polynomial with zeros #a#, #b# and #c# is

#(x-a)(x-b)(x-c)#

Hence a polynomial with zeros #i#, #-3i# and #3i# is

#(x-i)(x-(-3i))(x-3i)#

= #(x-i)(x+3i)(x-3i)#

= #(x-i)(x^2+9)#

= #x^3-ix^2+9x-9i#

Here leading coefficient (of #x^3#) is already one.

Hence, the polynomial with zeros #i#, #-3i# and #3i# is #x^3-ix^2+9x-9i#