Question

State how many imaginary and real zeros the function has.

f(x) = x^3 - 20x^2 + 123x - 216

Answer 1

familiar wid Descartes rule of signs ?

Answer 2

I am familiar with it but need to be reminded

Answer 3

ok take f(x)

how many sign changes do u see ?

Answer 4

2?

Answer 5

try again

Answer 6

u need to see how many times the sign is changing

Answer 7

f(x) = x^3 - 20x^2 + 123x - 216
^ ^ ^

Answer 8

Okay 3

Answer 9

good :), now find f(-x), and count sign changes

Answer 10

f(x) = x^3 - 20x^2 + 123x - 216

f(-x) = ?

Answer 11

So do the inverse?


I'm stupid forgive me.

Answer 12

hey first tim eyou doing this, i can understand...

Answer 13

to find f(-x), just replace all x with -x

Answer 14

f(x) = x^3 - 20x^2 + 123x - 216

f(-x) = (-x)^2 - 20(-x)^2 + 123(-x) - 216

Answer 15

x-20x-123-216 or am I completely off

Answer 16

you're right ! but i was wrong

Answer 17

f(x) = x^3 - 20x^2 + 123x - 216

f(-x) = (-x)^3 - 20(-x)^2 + 123(-x) - 216

Answer 18

i did a typo, its (-x)^3, its not (-x)^2

Answer 19

f(x) = x^3 - 20x^2 + 123x - 216

f(-x) = (-x)^3 - 20(-x)^2 + 123(-x) - 216

= -x^3 - 20x^2 - 123x - 216

Answer 20

now tell me, how many sign changes u see in f(-x) ?

Answer 21

None?

Answer 22

Yes, so we conclude like this :-

3 sign changes in f(x), so number of positive zeroes = 3, or 1
0 sign changes in f(x), so number of negative zeroes = 0

so total number of real zeroes = 3 or 1

Answer 23

that gives number of imaginary zeroes = 0 or 2

Answer 24

see if that makes some sense

Answer 25

0 imaginary and 3 real?

Answer 26

0 imaginary and 3 real

or

2 imaginary and 1 real

Answer 27

Both are true.

Answer 28

Both are true according to Descarted rule of signs. But when we solve it we will see that "0 imaginary and 3 real" is the correct one.

Answer 29

Thank you so much, you are a champion.

Answer 30

omg thank you :) im not champion, you're the champion cuz you learning things very fast :)