Question

What are the possible numbers of positive real, negative real, and complex zeros of
f(x) = -7x4 - 12x3 + 9x2 - 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

@goformit100

Answer 2

like this ?
\(\large f(x) = -7x4 - 12x^3 + 9x^2 - 17x + 3\)

Answer 3

thought of rational root thm ?

Answer 4

yes thats right and im having trouble wrapping my head around it

Answer 5

oklet me see ^^

Answer 6

does the rational roots test solve it?

Answer 7

i guess yes lets try

Answer 8

but i think its for real mmm idk abt complex

Answer 9

i got plus or minus 1, 1/7, 3, 3/7

Answer 10

so we need to find p,q
\(\Huge q=\pm 1,\pm3\)
\(\Huge p=\pm 1,\pm7\)
so possible zeros
\(\Huge \frac{p}{q} =\pm 1,\pm3 ,\pm\frac{3}{7}, \pm \frac{1}{7} \)

Answer 11

ok lol

Answer 12

okay whats the next step?

Answer 13

mmm nw we need to check from equation ?

Answer 14

well for rational its done

Answer 15

we can eliminate d and c

Answer 16

also we can remove b

Answer 17

thank you(:

Answer 18

nop :D

Answer 19

?? Might be wandering off on this one. We are not asked to FIND the roots, only to COUNT them.

What are the possible numbers of positive real, negative real, and complex zeros of

f(x) = -7x4 - 12x3 + 9x2 - 17x + 3

Descartes Rule of Signs suggests that we count the sign changes of f(x)

--+-+ That's 3 changes. There are, therefore, 3 or 1 Positive Real Roots.

Descartes Rule of Signs suggests that we count the sign changes of f(-x)

-++++ That's 1 change. There must be, therefore, 1 Negative Real Root.

Since there are 4 total, there can be

3 Positive, 1 Negative, and 0 Complex
or
1 Positive, 1 Negative, and 2 Complex.

Answer 20

mmm it said what are not how many i guess

Answer 21

I agree that "possible numbers" could go either way. There we have both, in any case.

Answer 22

ic ... i liked ur method though

Answer 23

Never underestimate the power of something that can count! Always a good thing to know.

Answer 24

yeah !