anonymous
  • anonymous
MEDAL AND FAN!!!! Which of the following represents the zeros of f(x) = 3x3 − 10x2 − 81x + 28
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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UsukiDoll
  • UsukiDoll
\[f(x) = 3x^3-10x^2-81x+28 \] this?
UsukiDoll
  • UsukiDoll
if we need to find 0's then we need the rational root test.
UsukiDoll
  • UsukiDoll
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.

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More answers

anonymous
  • anonymous
is the answer 7, -4, 1/3
alekos
  • alekos
but the last root lies somewhere between 0 and 1 and I think 1/3 is pretty close
anonymous
  • anonymous
answer choices 7,-4,1/3 7,-4,-1/3 7,4,1/3 7,4,-1/3
UsukiDoll
  • UsukiDoll
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
anonymous
  • anonymous
im pretty sure it is the last choice
UsukiDoll
  • UsukiDoll
did you test it out?
anonymous
  • anonymous
kind of
UsukiDoll
  • UsukiDoll
because there's a negative root.. and that number is not -1/3
UsukiDoll
  • UsukiDoll
so that knocks out two choices.
anonymous
  • anonymous
that means it is the third choice because after you test it out it gives you the third choice
UsukiDoll
  • UsukiDoll
no
alekos
  • alekos
negative root is x=-4
UsukiDoll
  • UsukiDoll
mhm ^
anonymous
  • anonymous
oops i think i know the answer for this question can you help me with another
UsukiDoll
  • UsukiDoll
yeah sure. you actually had the right answer 10 minutes ago XD
anonymous
  • anonymous
Which of the following is a polynomial with roots 5, 4i, and −4i
anonymous
  • anonymous
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
UsukiDoll
  • UsukiDoll
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.
anonymous
  • anonymous
so plug 5 for each one
UsukiDoll
  • UsukiDoll
try let x = 5 for the second function
UsukiDoll
  • UsukiDoll
yeah for each one, but I think I've weeded it out x=5 for the second function
anonymous
  • anonymous
i think i can take out the 2nd one and also the the first one
UsukiDoll
  • UsukiDoll
first one is nasty... x.x
anonymous
  • anonymous
so that is definitely eliminated
UsukiDoll
  • UsukiDoll
oh yeah... not to mention that the real root is x=1... not what we need.
anonymous
  • anonymous
the answer is the third one
UsukiDoll
  • UsukiDoll
umm are you sure?
anonymous
  • anonymous
im pretty sure
UsukiDoll
  • UsukiDoll
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
anonymous
  • anonymous
im feeling that my work shows that it is the answer
anonymous
  • anonymous
the last one
UsukiDoll
  • UsukiDoll
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
anonymous
  • anonymous
yes
UsukiDoll
  • UsukiDoll
then that's the function. since the result became 0... for x = 5... then the roots x =4i, -4i work as well.
anonymous
  • anonymous
thanks
UsukiDoll
  • UsukiDoll
you're welcome :)

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