Question

Which of the following is true
A polynomial of degree 4 has 4 unique zeros
A polynomial of degree 5 has at least 1 real zero
A polynomial of degree 2 has at least 1 real zero
Please show work and explain to me how each works

Answer 1

not the first one you can have x^4
not the third one you can have x^2 + 8 + 1 roots x = +-3i

Answer 2

http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

Answer 3

the second one works because only complex roots can only come in pairs, so you can have
4 complex roots and 1 real root or
2 complex roots and 3 real roots or
5 real roots

Answer 4

but I am confused

Answer 5

where?

Answer 6

without a calculator, how do you see the zeros or roots as your site says?

Answer 7

The question does not ask for you to find the zeros it just asks if there is any, and you can use synthetic division for the x's raised to power 5.

Answer 8

okay so please show me

Answer 9

Show you how to use synthetic division? or?

Answer 10

how you got the answers

Answer 11

like show me the process through synthetic division

Answer 12

I got the answers from my differential equations class.... here is a website that I used to get a refresher on it though. http://www.purplemath.com/modules/synthdiv.htm