Question

I don't know how to do this question...

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

Answer 1

solve for x or factor?

Answer 2

well actually I read it wrong it says: What are the possible number of positive, negative, and complex zeros of f(x) = -2x3 - 5x2 + 6x + 4 ?
Use complete sentences to explain the method used to solve this equation.

Answer 3

"possible" right, not actual

Answer 4

yes

Answer 5

\[f(x) = -2x^3 - 5x^2 + 6x + 4 \] for the possible positive zeros, you are looking for the change in sign of the coefficients
do you know what that means?

Answer 6

yes, so there would be 1 change right?

Answer 7

exactly
that means there must be one positive zero

Answer 8

now for the negative ones, look for the number of changes of sign of \(f(-x)\)

Answer 9

first off of course you need \(f(-x)\)
do you know what that is?

Answer 10

yes it would be changing all the signs opposite right? so there would still be only 1 change?

Answer 11

no it does not change all the signs
you have to replace \(x\) by \(-x\) and see what you get

Answer 12

the sign of the coefficients of the odd powers will change, but the coefficients of the even powers will remain the same, as will the constant

Answer 13

step one is \[f(-x)=-2(-x)^2-5(-x)^2+6(-x)+4\]

Answer 14

ok typo there, step one is \[f(-x)=-2(-x)^3-5(-x)^2+6(-x)+4\]

Answer 15

so it would be 2x^3+5x^2-6x+4

Answer 16

no

Answer 17

the \(2x^3\) is right
so is the \(-6x\) and of course the \(+4\)

Answer 18

but \((-x)^2=x^2\) so \(-5(-x)^2=-5x^2\)

Answer 19

oh i forgot to square the x's

Answer 20

so what do you get, and how many changes of sign does it have?

Answer 21

you'd have 2x^3-5x^2-6x+4. there would be 2 changes

Answer 22

yes so either 2 negative zeros, or no negative zeros (you count down by twos)

Answer 23

in fact this one has two negative zeros and one positive one

Answer 24

so there are no complex zeros?

Answer 25

not for this one
of curse there can be at most 3 total since it is a poly of degree 3
choices would be
a) one positive two complex or
b) one positive, two negative

Answer 26

okay

Answer 27

Thank you so much!

Answer 28

yw