Question

Find the roots of the polynomial equation.

2x^3 + 2x^2 – 19x + 20 = 0


3+i/2 , 3-i/2 , -4
-3+2i/2 , -3-2i/2 , 4
-3+i/2 , -3-i/2 , -4
3+2i/2 , 3-2i/2 , 4

Answer 1

so, you know how to do synthetic division?

Answer 2

No , im home-schooled . I dont get taught this stuff . its really hard for me because i dont have teacher . . .

Answer 3

no worries, its about as easy as the rational root test and they go together anyways.

Answer 4

That's gotta be good , rite ? lol

Answer 5

to start you need to do the rrt and find all rational roots. In this case there are 12 possible roots, but because its multiple choice we can eliminate the root to be either -4, or 4.

Answer 6

rite.. :)
its a long process...

Answer 7

now I have to draw

Answer 8

ok , (:

Answer 9

alright so this is synthetic division. You take the polynomial and divide it by the root you want to test. If it is legit, then the remainder (84 above) should be zero.

Its not really division though. To start you take the 2 bring is down and times is by 4 giving you 8. Then 8 plus 2 is 10, times by 4 is 40, and so on.

Answer 10

because the remainder is 84, it is safe to say that 4 is not a root.

Answer 11

ok, i seee that . so it has to be a or c . .. .

Answer 12

yep, I tested -4 and it works

Answer 13

when you do negative 4 you get,
_______________________
-4 | 2 2 -19 20
-8 24 -20
------------------
2 -6 5 0

Answer 14

yes i seee. so then how do you find out about the 3+i/2 part ?

Answer 15

the bottom is important because this is your new polynomial.

2x^2 - 6x + 5=0

Find the roots of that by doing the quadratic equation.

Answer 16

you know that by heart right? ;)

Answer 17

dont you do it how you showed me on my last problem ?

Answer 18

o well, the roots that you have left are not rational.

Answer 19

so , what does that mean ?

Answer 20

the rational root test can only test for roots that are whole numbers. Square roots and imaginary numbers cant be done that way.

Answer 21

So , then how are we supposed to figure the answer out ?

Answer 22

quadratic equation.

Answer 23

best tool in finding roots hands down

Answer 24

dont think , im a slow , lol . but whats that equation. I dont know it by heart .

Answer 25

\[\frac{ -b \pm \sqrt{b ^{2}-4ac} }{2a }\]

Answer 26

know how to use it?

Answer 27

ughhh , i suck at that ^ -____-

Answer 28

yeah, it generally sucks all around...

best thing to do is convert your polynomial into something a bit easier to manage. Like this

Answer 29

x^2 - 3x + 5/3 = 0

(divide the whole thing by 3)

Answer 30

3 +/- sqrt(9 - 4(5/3)) all over 2

Answer 31

do you have to choose plus or minus ?

Answer 32

nope, they are both included. You will have at least two roots using the quadratic equation.

Answer 33

i just tried to type that in my calc & it said syntax error.

Answer 34

whoa, ok. Im back.

So I goofed above. The equation is 3 +/- sqrt( 9 - 4(5/2)) all over 2
but if you plug this into your calc it wont work because of the imaginary number. You will have to simplify on paper.

Answer 35

i just messed up badly . i got 3 +/- (-3-10)

Answer 36

thats not too bad, you just have to square the 3 and then your all set

Answer 37

what do you mean ? how ?

Answer 38

3 +/- (9-10)

Answer 39

im sooo confused .

Answer 40

sorry. you will have 3+/- sqrt(9-10)
this is 3+/- sqrt(-1)
which is 3+/- i

Answer 41

all of this is divided by 2. SO i think your answer will be c

Answer 42

i thought it would of been a . im terrible at math . lol

Answer 43

no worries. Practice is the key.

Answer 44

well thank you sooo much , i appreciate it (;

Answer 45

your welcome. Learning math at home without a teach can be hard so hit me up if you need more help.