Question 766631: f(x)=3x^(4)+5x^(3)+7x^(2)+3x-2
find all zeros including complex zeros
write f(x0 in completely factored form Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! f(x)=3x^(4)+5x^(3)+7x^(2)+3x-2
find all zeros including complex zeros
***
use rational roots theorem:
...0...|.....3......5.......7.......3......-2........
...1...|.....3......8......15.....18......16(there is a root between zero and one) (change in sign)
.1/3.|.....3......6.......9.......6........0(1/3 is a root)
=============================
.-1...|.....3......3.......6.......0 (- 1 is a root)
f(x)=(x+1)(3x-1)(3x^2+3x+6)
3x^2+3x+6=0
use quadratic formula:
a=3, b=3, c=6
x=[-3±√(3^2-4*3*6)]/2*3
x=(-3±√-63)/6
x=(-3±3√7i/6
x=(-1±√7i)/2
real zeros are: 1/3 and -1
complex zeros are: (-1+√7i)/2 and (-1-√7i)/2
(