How do you find a third degree polynomial given roots #6# and #3-2i#?

1 Answer
Jul 12, 2017

Answer:

#f(x)=x^3-12x^2+49x-78#

Explanation:

#"note that"#

#"complex roots occur in conjugate pairs"#

#3-2i" is a root " rArr3+2i" is also a root"#

#rArrf(x)=(x-6)(x-(3-2i))(x-(3+2i))#

#color(white)(rArrf(x))=(x-6)((x-3)+2i))((x-3)-2i))#

#color(white)(rArrf(x))=(x-6)((x-3)^2-4i^2)#

#color(white)(rArrf(x))=(x-6)(x^2-6x+13)#

#color(white)(rArrf(x))=x^3-12x^2+49x-78#