Question

can someone explain this to me? how do i do this??

Answer 1

You know the descartes rule?

Answer 2

not really

Answer 3

brb

Answer 4

It says find the number of sign changes in f(x) for the POSSIBLE number of +ve roots. And find the number of sign changes in f(-x) for the POSSIBLE number of -ve roots.

So here
4x^3 + x^2 + 10x – 14
Going from 4x^3 to x^2 the sign remains same, +ve.
x^2 to 10x, sign remains same, +ve.
10x to -14, sign changes, +ve to -ve.
So there is only 1 possible real root. You cant have complex roots here, since they occur in pairs.

Do this for f(-x)
-4x^3 +x^2 - 10x -14
So you see, here there are 2 sign changes. One from -4x^3 to x^2 and another from x^2 to -10x. So 2 is the number of possible -ve real or complex roots.

Answer 5

Answer would be (b).

Answer 6

Just to clarify, f(x) = 4x^3 + x^2 + 10x – 14.. for f(-x) you just replace x with -x in every term.

Answer 7

Done?

Answer 8

i don't get it :/

Answer 9

Which part?

Answer 10

all of it :c

Answer 11

See you look at f(x), see the number of SIGN CHANGES going from one term to another. Number of sign changes=number of possible roots.
When you do this for f(x) they are number of positive roots, you do the same thing for f(-x) they are possible -ve roots.

Answer 12

f(x) = 4x^3 + x^2 + 10x – 14 only has one sign change...so that wouldm ean that there's only 1 possible positive root??

Answer 13

would mean*

Answer 14

Absolutely. F(-x) has two, that means two possible negative real/complex roots.

Answer 15

f(-x) = 4(-x)^3 + (-x)^2 + 10(-x) – 14
f(-x) = -4x^3 - x^2 - 10x -14???

Answer 16

there wouldn't be any sign changes??? am i doing this wrong??

Answer 17

4(-x)^3 + (-x)^2 + 10(-x) – 14 Correct.
But (-x)^2=x^2.

Answer 18

hmmmmm ok

Answer 19

so 2 sign changes means there's 2 possible negative roots?

Answer 20

yes.

Answer 21

ok. thank you :]

Answer 22

You're welcome.
Night/morning. Its already 6. lol.
bbye.

Answer 23

bye ♥