How do you write a polynomial with zeros 2,# 4+sqrt5#, # 4-sqrt5#?

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Answer 1 · 2016-02-07T17:52:33

#x^3-10x^2+27x-22#

The polinonimal will be the result of

#(x-2)(x-4-sqrt(5))(x-4+sqrt(5))#

#(x-2)((x-4)^2-5)#

#(x-2)(x^2-8x+16-5)#

#(x-2)(x^2-8x+11)#

#x^3-8x^2+11x-2x^2+16x-22#

#x^3-10x^2+27x-22# or a multiple of it:

#a(x^3-10x^2+27x-22)#