Question

Can you explain to me how to solve this please??



What are the possible number of positive, negative, and complex zeros of f(x) = -2x^3 - 5x^2 + 6x + 4 ?

Answer 1

r u allowed to use a graphing calculator?

Answer 2

or have u been taught the quadratic formula?

Answer 3

im not sure I have to show work.

Answer 4

quadratic formula

Answer 5

sorry quadratic wont work for this.....do u know how to take derivatives...or what is the chapter u r learning for this hw....as there r several ways to do this

Answer 6

can anyone help me?!

Answer 7

c if i answer a diffrent way that is not based on ur level of calculus ull be caught

Answer 8

well its Algebra 2 if that helps?

Answer 9

hmmm have you covered Descartes Law of Signs?

Answer 10

yes!

Answer 11

ok, then let's take a peek at the function

f(x) = -2x^3 - 5x^2 + 6x + 4
- - + +
no yes no

so it changes only ONCE in signs, from - to +
that means it has only 1 real POSITIVE root

Answer 12

yes..

Answer 13

now let's check for negative ones by using f(-x)

f(-x) = +2x^3 - 5x^2 - 6x + 4
yes no yes

so it changed TWICE in signs, that means it has 2 or 0 real NEGATIVE roots

Answer 14

so the degree of the polynomial is 3, that means 3 roots
so it will have either
1 positive and 2 negative ones, no room for complex there, so no complex ones
1 positive and 0 negative ones, room enough for 2 complex, so 2 complex ones

Answer 15

THANK YOU HANK YOU THANK YOU!

Answer 16

yw