Question

Determine the zeros of f(x) = x4 – x3 + 7x2 – 9x – 18

Answer 1

Can someone explain how to solve

Answer 2

find one root by inspection

Answer 3

try if -1 is a root

Answer 4

Do you know the Rational Root theorem?

Answer 5

Basically, try all the factors of +- 18

Answer 6

Since the constant term is -18, and the leading coefficient is 1, try zeros of
1, -1
2, -2
3, -3
to start with using synthetic division.

Answer 7

just find one root, divide it. you would get a cubic which is easy to factor

Answer 8

Once you have one, divide the polynomial by (x-root) and simplify.

Answer 9

find one root first, we can do it together

Answer 10

Once you have zero remainder in synthetic division, you found a zero and the quotient is the the polynomial reduced by 1 degree.

Answer 11

take ur time

Answer 12

try the small ones 1 and -1 first

Answer 13

you dont want to waste time trying all combinations, just find one root. and we cna take it from there

Answer 14

ok

Answer 15

Also, if you just evaluate the function at x = 1, -1, 2, -2, etc, if y = 0, then the x value you used is a zero of the polynomial.

Answer 16

synthetic division is always faster than zero remainder theorem

Answer 17

So for the polynomial function is will be x^3 -2x^2 +9x -18

Answer 18

you foind that -1 is a root is it ?

Answer 19

Yes

Answer 20

and synthetic division gave u x^3 -2x^2 +9x -18

Answer 21

Yes

Answer 22

x^3 -2x^2 +9x -18

lets try to factor this by grouping

Answer 23

x^3 -2x^2 +9x -18

x^2(x-2) + 9) + 9(x-2)

Answer 24

rest is bit easy

Answer 25

Ah, I see what you did

Answer 26

I was trying to do grouping at the very beginning before using synthetic

Answer 27

So only after synthetic I do this, correct?

Answer 28

sorry typo there. it should be

x^3 -2x^2 +9x -18

x^2(x-2) + 9(x-2)

Answer 29

even i tried to group if before doing synthetic, it didnt work

Answer 30

so we're forced to find one root using synthetic

Answer 31

You can't use factoring by grouping with 5 terms.

Answer 32

every polynomial is different, we need to try what works easily. thats all

Answer 33

you can factor 5 terms by making them 6

Answer 34

thats right

Answer 35

we got 4 zeroes

Answer 36

-1 in the very beginning

Answer 37

and the cubic will give u 3 more zeroes

Answer 38

dont forget the i

Answer 39

x^3 -2x^2 +9x -18

x^2(x-2) + 9(x-2)

(x^2+9)(x-2)

x = 2, 3i, -3i

Answer 40

Sometimes a zero appears more than once in a polynomial equation. For example, if a polynomial factors into:
(x - 5)(x - 5)(x - 7)(x - 7) = 0
Then you have two roots x = 5 and two roots x = 7.
This is called x = 5, multilicity 2, x = 7 multiplicity 2.

Answer 41

okay good

Answer 42

Also thank you for your help!

Answer 43

yw !

Answer 44

In this case, you have two real roots and two complex roots. Notice that the complex roots are a pair of complex conjugates.

Any polynomial that has real coefficients and has complex roots, the complex roots are always pairs of complex conjugates.

Answer 45

wlcm

Answer 46

you are a root because you're doing polynomials is it... or you're doing polynomianls because you're a root :P

Answer 47

Haha

Answer 48

jk.... have fun :D

Answer 49

You too :D