## How many complex zeros does the polynomial function have? f(x)=−3x^6−2x^4+5x+6

Question

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.Morbi adipiscing gravdio, sit amet suscipit risus ultrices eu.Fusce viverra neque at purus laoreet consequa.Vivamus vulputate posuere nisl quis consequat.

## Answers ( No )

one way would be to factor

I can’t factor it so we will have to use Descartes’ Rule of Signs which is helpful for finding how many real roots you have

it goes like this:

for a polynomial with real coefients, consider .

after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have

We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root

to get the negative roots, we evaluate f(-x) and see how many times the root changes

signs are (-, -, -, +). there was 1 change in sign

so the function has 1 real negative root

a total of 2 real roots

a function of degree can have at most, roots

our function is degree 6 so it has 6 roots

if 2 are real, then the others must be complex

6-2=4 so there are 4 complex roots

you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots