Question

How do you write a polynomial in standard form given zeros -4, 1 - i, and 1 + i?

Answer 1

`x^3+2x^2-6x+8=0`.

Explanation:

For a cubic equation, use
`x^3-(a+b+c)x^2+(bc+ca+ab)x-abc=0` for the equation whose roots are a, b and c. Here, a+b+c=-2, bc +ca+ab=-2 and abc=-8.

Also, if the roots are `a and b+-ic`, the equation is
`(x-a)((x-b)^2+c^2)`.
Here, it is `(x+4)((x-1)^2+1^2)=0`,