Question

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

Answer 1

`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`