zeros of 1-i, 1+i, and 3
We need to find a third degree polynomial
if we are given with three zeros p, q and r then polynomial can be written as
a (x-p) (x-q) (x-r)
Leading coefficient is -7
So a= -7
Replace all the zeros
-7 ( x- 3) (x-(1-i)) (x-(1+i))
-7(x-3)(x-1+i) (x-1-i)
[tex]-7 (x - 3) (x^2 - 2 x + 2)[/tex] ( the value of i^2 = -1)
Multiply (x-3) inside the second parenthesis
[tex]-7 (x^3 - 5 x^2 + 8 x - 6)[/tex]
Now multiply -7 inside the parenthesis. the required polynomial is
[tex]-7x^3 + 35x^2 - 56x + 42[/tex]
