Question

??

Answer 1

for part I the max number of roots is equal to the degree

Answer 2

3?

Answer 3

the degree is the highest exponent

Answer 4

4

Answer 5

good

for part IIa) count the sign changes in H(x)

Answer 6

3?

Answer 7

so 4 maximum positive real roots

Answer 8

okay so for part iii a\[4(-x)^4-5(-x)^3+2(-x)^2+x+5\]

Answer 9

good, now simplify this and count the number of sign changes in the simplified expression

Answer 10

um 2?

Answer 11

4x^4 + 5x^3 + 2x^2 + x + 5

^ how many sign changes?

Answer 12

not 2?

Answer 13

no, not 2

count the number of sign changes in the above expression

Answer 14

from the original right?

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
4x^4 + 5x^3 + 2x^2 + x + 5

^ how many sign changes?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 16

the one after we plugged in (-x)

Answer 17

4

Answer 18

notice how all the signs are positive

Answer 19

yeah

Answer 20

so how many sign changes are there if they all are positive?

Answer 21

1

Answer 22

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
4x^4 + 5x^3 + 2x^2 + x + 5

^ how many sign changes?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 23

after the 4x^4 it is a positive that's all i see

Answer 24

a sign change is defined as an instance where the sign changes from + to - or from - to +

with that being said, how many sign changes are there?

Answer 25

3

Answer 26

the first term is positive
the second term is positive (so no change)
the third term is positive (still no change)
the fourth term is positive (still no change)

so how many sign changes?

Answer 27

1

Answer 28

Ugh sorry

Answer 29

remember, for a sign change the sign has to switch from + to - or from - to +

Answer 30

so if they are all + how many sign changes?

Answer 31

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
the first term is positive
the second term is positive (so no change)
the third term is positive (still no change)
the fourth term is positive (still no change)

so how many sign changes?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 32

From this 1

Answer 33

notice how all the terms are positive

for something to count as a sign change, the sign MUST change from + to - or from - to +

but notice how we don't have any negative signs, so there must be __ sign changes

Answer 34

zero

Answer 35

good, zero sign changes and zero possible roots

for c) since total roots = 0 and positive roots can be at most 4, if we consider complex roots as doubles there can be either 4, 2, or 0 complex roots

Answer 36

so 4,2,0

Answer 37

yes

Answer 38

okay so for part IV

Answer 39

would it be the same answer?

Answer 40

c) should be 0 negative roots, IV should be 4/2/0 complex roots