Question #9a361

1 Answer
Jim G.
Dec 13, 2017

#x^4-2x^3+14x^2-18x+45#

Explanation:

#"complex roots occur as "color(blue)"conjugate pairs"#

#x=1-2i" is a root "rArrx=1+2i" is also a root"#

#x=3i" is a root "rArrx=-3i" is also a root"#

#rArrp(x)=(x-3i)(x+3i)(x-1+2i)(x-1-2i)#

#color(white)(rArrp(x))=(x^2-9i^2)((x-1)^2-4i^2)#

#•color(white)(x)[i^2=(sqrt(-1))^2=-1]#

#=(x^2+9)(x^2-2x+1+4)#

#=(x^2+9)(x^2-2x+5)#

#=x^4-2x^3+5x^2+9x^2-18x+45#

#=x^4-2x^3+14x^2-18x+45#

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