How do you write a polynomial function in standard form with real coefficients whose zeros include 3, 5i, and -5i?

1 Answer
May 7, 2016

Answer:

The polynomial function in standard form with real coefficients whose zeros include #3#, #5i#, and #-5i# is #x^3-3x^2+25x-75#

Explanation:

A polynomial function with zeros as #a#, #b# and #c# would be

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

Hence a polynomial function with zeros as #3#, #5i# and #-5i# would be

#(x-3)(x-5i)(x-(-5i))# or

#(x-3)(x-5i)(x+5i)# or

#(x-3)(x^2-(5i)^2)# or

#(x-3)(x^2-25i^2)# or

#(x-3)(x^2+25)# or

#x^3-3x^2+25x-75#