Question

Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

x³-4x²-7x+28=0

a. two or zero
b. three or one
c. one
d. two

Answer 1

it has three roots 4, 7,7
two roots are the same so
option d

Answer 2

it has 3 roots
x= -2.64...
x= 2.64...
x=3

Answer 3

It just said it was a.

Answer 4

answer is d

Answer 5

I'm doing an online course and it said a after I put in d.

Answer 6

why?

Answer 7

it didn't explain why, so I have no clue :/

Answer 8

i have wrote the root and just two are positive

Answer 9

descartes rule of sign for this one

Answer 10

it says
"possible number of positive real solutions"

Answer 11

not asking for the actual number of positive zeros. there are two "changes in sign" in this
\[x³-4x²-7x+28=0\]
from
\[x^3\] to
\[-4x^2\] is positive to negative, and then another change in sign from
\[-7x\]to
\[28\] therefore there are either 2 positive real zeros or none

Answer 12

there is a nice explanation of descartes rule of sign here
http://www.purplemath.com/modules/drofsign.htm

Answer 13

i've got it . that site was so helpful