Question

Create your own polynomial with a degree greater than 2. Find the zeros of the function.

could someone walk me through on how to do this? I don't get what "find the zeros" means..

Answer 1

mathematicians use different words for the same thing
zeros = roots = x intercepts

Answer 2

I tend to use the word roots more than 'zeros'
so we can look at a factored form a polynomial, in terms of its 'roots'

y = a ( x - r1) (x-r2) (x-r3)... (x-rn) , where r1,r2,..rn are roots

Answer 3

so you want a polynomial of degree greater than 2, so you will need at least 3 factors

y = a ( x - r1 ) ( x - r2) ( x - r3) , now pick any values for r1, r2, r3 and you can let 'a' equal 1 , since thats easiest

Answer 4

sorry, i still don't really get what you're saying
:(

Answer 5

i had another question that said "Using complete sentences, explain how to find the zeros of the function f(x) = 2^3 – 9x + 3." i wrote that you would try to find the x values in this to check if they came out to 0, is that right?

Answer 6

function f(x) = 2^3 - 9x + 3.

Answer 7

is there an x missing

Answer 8

f(x) = 2x^3 - 9x + 3.

Answer 9

ok, thats a cubic polynomial

Answer 10

it is difficult to factor these generally, but sometimes it has nice x intercepts (roots) which I find by graphing it

Answer 11

alternatively you can use rational roots theorem, but this theorem won't guarantee you rational roots exist

Answer 12

the theorem says *if* rational roots exist, then the roots will have such and such form

Answer 13

if f(p/q) = 0 , then p divides the constant coefficient and q divides the coefficient of the degree term

Answer 14

and check out wolfram, it does a lot of the tedious stuff.

here is what i will submit into wolfram
"solve 2^3 - 9x + 3= 0 " (this gives us the roots)

Answer 15

Wolfram gives me one real rational root
x = 11/9
http://www.wolframalpha.com/input/?i=solve+2^3+-+9x+%2B+3%3D+0

Answer 16

so now you can do synthetic/long division and factor out (x -11/9) ,

Answer 17

alternatively, you could use something called the cubic formula, but its probably outside the scope of your class or homework

Answer 18

and it would be overkill in this example to use cubic formula