How do you write a polynomial equation of least degree given the roots -3, -2i, 2i?

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Answer 1 · 2017-04-18T13:28:14

The polynomial is #x^3+3x^2+4x+8#

A polynomial equation of least degree given the roots #alpha, beta# and #gamma# is

#(x-alpha)(x-beta)(x-gamma)#

Hence, a polynomial equation of least degree given the roots #-3, -2i# and #2i# is

#(x-(-3))(x-(-2i))(x-2i)#

= #(x+3)(x+2i)(x-2i)#

= #(x+3)(x^2-(2i)^2)#

= #(x+3)(x^2-4i^2)#

= #(x+3)(x^2-4×(-1))#

= #(x+3)(x^2+4)#

= #x^3+3x^2+4x+12#