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

1 Answer
Apr 4, 2016

x^3+2x^2-6x+8=0x3+2x26x+8=0.

Explanation:

For a cubic equation, use
x^3-(a+b+c)x^2+(bc+ca+ab)x-abc=0x3(a+b+c)x2+(bc+ca+ab)xabc=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+-icaandb±ic, the equation is
(x-a)((x-b)^2+c^2)(xa)((xb)2+c2).
Here, it is (x+4)((x-1)^2+1^2)=0(x+4)((x1)2+12)=0,