Question

Part 1: What are the possible number of positive, negative, and complex zeros of f(x) = –2x3 – 5x2 + 6x + 4?
Part 2: Use complete sentences to explain the method used to solve this equation.

Answer 1

you can Use Descartes' Rules of Signs

Answer 2

positive is 1

Answer 3

not sure how though/.. can u explain?

Answer 4

to find the possible positive number look at the equation where the term change its sign
in the equation -5x^2 has negative sign the next term to it is 6x which is positive , therefore in the equation there is one only that change its sign,,
from negative to positive

Answer 5

@sar12 that is deacartes rule

Answer 6

right i got that so what else?

Answer 7

well so -2x3 goes to -5x2 which is not one?

Answer 8

so only one P, because of -5x^2 to +6x?

Answer 9

so u just change the opposite signs of everything in the equation for the negative?

Answer 10

yes
good, for negative just change f(x) to f(-x) and find how many change its terms, like this
[f(-x) = -2(-x)^3 -5(-x)^2 + 6(-x) + 4

Answer 11

the x to -x

Answer 12

so now we have 1 Positive, 1 negative?

Why dont we have 1 or 0? what does that have to do with anything anyway?

Answer 13

@sar12 so what did you get in negative???

Answer 14

1?

Answer 15

how i thought we are counting the sign changes?

Answer 16

yup im sorry its 1 xD

Answer 17

its ok, so why sometimes its like also 0 like 2 and 0?

Answer 18

http://www.purplemath.com/modules/drofsign.htm
to understand the whole concept of Descartes' Rules of Signs
I think this will help you a lot

Answer 19

ok thanks wait so what about the complex?

Answer 20

@traile what about the complex?

Answer 21

um so do u know? can u help me?

Answer 22

wahts a complex zero? I need help with that ....

Answer 23

get the roots of the equation
the answer is 2

Answer 24

2 complex zeros, equate the equation to zero then get the roots

Answer 25

get the roots, what is the roots? how to do u evaluate?

Answer 26

is it two or zero?

Answer 27

like Complex zeros: 2, 0 ?

Answer 28

Im not that sure but I think the answer is 2 or 0,
Complex 2 or 0

Answer 29

but dont u have to subtract by 2 if its like 2 or more?,

Answer 30

For example if there were two positive, then it would be 2 or 0...

Answer 31

so wait its the thrid degree so that is where u find the complex roots? how do u find the complex zeros?

Answer 32

A cubic, will have 3 roots, they may be repeated, complex, irrational or rational.

there is a root between x = -1 and x = 0

using the remainder theorem

P(-1) = 2 - 5 -6 + 4
= -5

P(0) = 4

try

P(-1/2) = 1/4 - 5/4 - 6/2 + 4
P(1/2) = 0

so x = -1/2 is a root

or (2x +1) is a factor

use polynomial division to find the quadratic solution



so\[ P(x) = (2x+1)(-x^2 -2x + 4)\]

you will need the general quadratic formula for the roots of the quadratic