Question

What are the possible numbers of positive real, negative real, and complex zeros of
f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3?

Positive Real: 3 or 1
Negative Real: 1
Complex: 2 or 0

Positive Real: 3 or 1
Negative Real: 2 or 0
Complex: 1

Positive Real: 1
Negative Real: 3 or 1
Complex: 2 or 0

Positive Real: 4, 2 or 0
Negative Real: 1
Complex: 0 or 1 or 3

Answer 1

you want to substitute values into f(x) to start
for example
f(1)
f(2)
f(-1)
etc until you find a value or two values that make f(x)=0
can you do this?

Answer 2

okay let me try and sorry for replying late my internet keeps going off

Answer 3

but what do i plug in for f(x)?

Answer 4

f(x)= -7x^4 - 12x^3 + 9x^2 - 17x + 3

so f(1) means replace all x terms with 1

Answer 5

okay so just to get this clear you want me to solve doing f(1) and f(2) and f(-1)

Answer 6

i want you to use the value the question has given you
Positive Real: 3 or 1
Positive Real: 4, 2 or 0

Answer 7

okay so

f(3) = -7x^4 - 12x^3 + 9x^2 - 17x + 3
f(3) = -7(3)^4 - 12(3)^3 + 9(3)^2 - 17(3) +3
f(3) = -7(81) - 12(27) + 9(9) - 17(3) +3
f(3) = - 567 - 324 + 81 - 51 + 3
f(3) = -858

Answer 8

like that?

Answer 9

yeah

Answer 10

okay and if f(x) doesn't equal 0 its not the correct answer?

Answer 11

oh ignore me

Answer 12

what?

Answer 13

i understood the question wrong

Answer 14

oh

Answer 15

okay so you know that the function is to the power of 4

Answer 16

therefore it has 4 possible roots

Answer 17

ok

Answer 18

you want to figure out, how many real it can have (pos or neg) and how many complex it has

Answer 19

idk how to do that? i missed a couple of days of school now she wants me to make it up over this spring break

Answer 20

@ganeshie8 can you help him ? I can't do it

Answer 21

thanks anyways