Question

MEDAL AND FAN!!!!
Which of the following represents the zeros of f(x) = 3x3 − 10x2 − 81x + 28

Answer 1

\[f(x) = 3x^3-10x^2-81x+28 \] this?

Answer 2

if we need to find 0's then we need the rational root test.

Answer 3

The Rational Roots Test (also known as Rational Zeros Theorem) allows us to find all possible rational roots of a polynomial. Suppose "a" is root of the polynomial P(x) that means P(a) = 0. In other words, if we substitute "a" into the polynomial P(x) and get zero it means that the input value is a root.
so we take the last term, 28, and find all factors of 28
which is 1,2,4,7,14,28. We also have to take the negative versions as well. So,
1,-1,2,-2,4,-4,7,-7,14,-14,28,-28

just plug these numbers into the equation and stop once you have a 0
there could be more than one root, just one, or none. If we don't have any roots, the test fails.

Answer 4

is the answer 7, -4, 1/3

Answer 5

but the last root lies somewhere between 0 and 1 and I think 1/3 is pretty close

Answer 6

answer choices
7,-4,1/3
7,-4,-1/3
7,4,1/3
7,4,-1/3

Answer 7

hmmm....
let x = 7,4, or -4 and plug it into the equation ... one of them has to produce a zero .we may have to go further like long division to grab the remaining roots

Answer 8

im pretty sure it is the last choice

Answer 9

did you test it out?

Answer 10

kind of

Answer 11

because there's a negative root.. and that number is not -1/3

Answer 12

so that knocks out two choices.

Answer 13

that means it is the third choice because after you test it out it gives you the third choice

Answer 14

no

Answer 15

negative root is x=-4

Answer 16

mhm ^

Answer 17

oops i think i know the answer for this question can you help me with another

Answer 18

yeah sure. you actually had the right answer 10 minutes ago XD

Answer 19

Which of the following is a polynomial with roots 5, 4i, and −4i

Answer 20

f(x) = x^3-5x^2+20x-16
f(x) = x^3-5x^2+16x-80
f(x)=x^3-20x^2+5x-16
f(x) = x^3-16x^2+80x-5

Answer 21

wow... it's like we have to use the roots given and plugging in it into the function
having x = 5 will make it easier though.

Answer 22

so plug 5 for each one

Answer 23

try let x = 5 for the second function

Answer 24

yeah for each one, but I think I've weeded it out
x=5 for the second function

Answer 25

i think i can take out the 2nd one and also the the first one

Answer 26

first one is nasty... x.x

Answer 27

so that is definitely eliminated

Answer 28

oh yeah... not to mention that the real root is x=1... not what we need.

Answer 29

the answer is the third one

Answer 30

umm are you sure?

Answer 31

im pretty sure

Answer 32

the real root I'm getting for that third choice is really bad ... same with the imaginary... the real root is approx.. 20.. we need x = 5,4i,-4i cross that out

Answer 33

im feeling that my work shows that it is the answer

Answer 34

the last one

Answer 35

try plugging x = 5 for the second function you have and tell me if your result is 0
f(x) = x^3-5x^2+16x-80

Answer 36

yes

Answer 37

then that's the function. since the result became 0... for x = 5... then the roots x =4i, -4i work as well.

Answer 38

thanks

Answer 39

you're welcome :)