Question 1201671: Use the given zero to find the remaining zeros of the polynomial function
P(x) =2x^3-5x^2+6x-2; 1+i Found 2 solutions by mananth, ikleyn:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! P(x) =2x^3-5x^2+6x-2; 1+i
There have to be three factors
1-i is the conjugate of 1+i is also a root
(x-(1+i))(x-(1-i))
= x^2-x(1-i)-(1+i)x+1^2-i^2
=x^2 -x +xi -x-xi+1+1
= x^2 -2x +2
You can divide by co-efficient form
= 2x-1
2x-1=0
x=1/2
The factors are(1+i),(1-i),(1/2)
Since (1+i) is a root, the conjugate (1-i) is the root, too.
Using Vieta's theorem, we can write then that the sum of the roots is =
(1+i) + (1-i) + r = , where "r" is the third root,
or
2 + r = , r = - 2 = . ANSWER
