How do you write the simplest polynomial function with the zeros 2i, -2i and 6?

1 Answer
Nov 14, 2016

Answer:

Please see the explanation.

Explanation:

The factor that corresponds to the zero, #2i#, is #(x - 2i)#.
The factor that corresponds to the zero, #-2i#, is #(x + 2i)#.
The factor that corresponds to the zero, #6#, is #(x - 6)#.

Collect the factors into an equation:

#y = (x - 2i)(x + 2i)(x - 6)#

We can use the pattern, #(a - b)(a + b) = a^2 - b^2#, to multiply the first two factors:

#y = (x^2 - 4i^2)(x - 6)#

Use the property #i^2 = -1# to simplify the first factor:

#y = (x^2 + 4)(x - 6)#

Use the F.O.I.L. method to multiply the remaining factors:

#y = x^3 - 6x^2 + 4x - 24#