anonymous
  • anonymous
how do you find the rational and real roots? x^7+3x^6-5x^2-3x-5=0
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
trial and error.. alot of it lol
anonymous
  • anonymous
possible rational roots?
amistre64
  • amistre64
last# ----- helps to narrow it down fisrt#

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More answers

anonymous
  • anonymous
Rational root test, fundamental theorem of algebra, synthetic division
amistre64
  • amistre64
i was thinking of writing a javascript to solve these things ;)
anonymous
  • anonymous
make a fraction, numerator must divide 5, denom must divide 1, so only choices are \[\pm1, \pm 5\]
anonymous
  • anonymous
if you can write javascript to find the roots of a poly of degree 7 you would be world famous and galois would have been mistaken.
amistre64
  • amistre64
no, not all the roots; but the integer and rational roots that could be determined from this lol
anonymous
  • anonymous
i know i am being silly. you meant to find possible rational roots.
anonymous
  • anonymous
how do you find the real roots?
amistre64
  • amistre64
might be able to work it inside out and complete squares to find all roots .... i wonder
anonymous
  • anonymous
there is no algorithm for finding the roots of a poly of degree seven.
anonymous
  • anonymous
only 1 - 4. that is it. and the one for 3 is a page and the one for 4 is a wall.
amistre64
  • amistre64
well, you could do the Newton Rhapsody method to find 1 root and narrow it down ..... perhaps ?
anonymous
  • anonymous
i would try 1, -1, 5 and -5 and see if any work. then you can use synthetic division to reduce. i can see that 1 does not work since \[f(1)=1+3-5-2-5\]
amistre64
  • amistre64
make sure you include your zero place holders
anonymous
  • anonymous
\[f(-1)=-1+3-5+3-5=-1\]
anonymous
  • anonymous
well we have to find one first.
anonymous
  • anonymous
if you have a decent calculator check \[f(5)\]
amistre64
  • amistre64
syntheitc can find them as well; but brute calculating is always a good option lol
anonymous
  • anonymous
ok i will divide see if i get 0
watchmath
  • watchmath
Newton-Rhapsody :D :D
anonymous
  • anonymous
newton rhapsody in blue
anonymous
  • anonymous
5 doesn't work
anonymous
  • anonymous
and neither does -5 unless i made a mistake
amistre64
  • amistre64
-5| 1x^7 +3x^6 +0 +0 +0 -5x^2 -3x -5 0 -5 10 -50 250 -1250 6275 ------------------------------------- 1 -2 10 -50 250 -1255 ...... no mistake lol
amistre64
  • amistre64
D's sign change tells us what ...... do we include zeros as a sign change?

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