Question

how many positive. negative and complex zeros are in this equation? x^3+17x^2+72x-90 ?

Answer 1

you mean actual ones or possible ones?

Answer 2

whats the difference between them? the question just says "your function has _______ positive/ negative/ complex zeros"

Answer 3

oh in this case you would simply graph

Answer 4

one positive, 2 complex

Answer 5

how? my lesson doesnt say to graph. r

Answer 6

i thought maybe you were supposed to use descartes rule of sign

Answer 7

yeah i am

Answer 8

ok, but descartes rule of sign tells you the POSSIBLE number of positive, negative, and complex roots

Answer 9

we start with
\[f(x)=x^3+17x^2+72x-90\] and see only one change in sign, from +72 to -90

Answer 10

this tells you there is one postive root

Answer 11

now replace x by -x to get
\[f(-x)=(-x)^3+17(-x)^2+72(-x)-90\]
\[f(x)=-x^3+17x^2-72x-90\] and here i count two changes in sign

Answer 12

from -1 to +17 and from +17 to -72
that means either there are two negative roots, or no negative roots

Answer 13

so your possibilites are
1) one postive, two negative
2) one postive, two complex

Answer 14

it is a poly of degree 3 so there must be 3 (including the complex ones) and since it is of odd degree there must be one real one
but other than that, you don't know unless you graph or check somehow

Answer 15

if it was not clear what i meant, there is an excellent explanation here
http://www.purplemath.com/modules/drofsign.htm

Answer 16

i understand where it talks about the number of sign changes but it also says to subtract 2 if possible. thats what i dont understand

Answer 17

if there are say 5 changes in sign for f(x) then there are 5 or 3 or 1 positive zero

Answer 18

if there are 4 changes in sign for f(x) then either 4 or 2 or none. that is what it is telling you

Answer 19

so it goes by odd numbers?