Question

How many possible positive real zeros are there?

Answer 1

There are 3, right?

Answer 2

The maximum number of possible real roots is equal to the degree of the polynomial.
The degree of the polynomial is the highest exponent of x.

Answer 3

Ok, so there are 4. Thank you!

Answer 4

YW

Answer 5

it does say "positive" right?

Answer 6

for that you need descartes rule of sign

Answer 7

Yes, possible positive zeros.

Answer 8

ok count the changes in sign of the coefficients

Answer 9

You should know that, in this case, there is at least one double root.

Answer 10

\[f(x)=8x^4-72x^3+44x^3\] is all i see
is there any more of this?

Answer 11

actually i see \[f(x)=8x^4-72x^3+144x^2\] is that it?

Answer 12

or is there some other stuff not visible
there are not 4 possible positive real zeros for this one

Answer 13

No, that's the whole thing.

Answer 14

ok

Answer 15

then it pretty clearly factors as \[8 x^2 (x^2-9 x+18)\]

Answer 16

actually it factors more, but nvm that for a second

Answer 17

it has 0 as a zero with multiplicity 2 (that is because of the \(x^2\) in the front

Answer 18

there are two changes in sign on the coeffients
the coefficients are \[1,-9,18\] goes from plus to minus,(one change) then minus to plus (another change)

Answer 19

that means there are either 2 or no positive zeros
count the changes in sign, then count down by two