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trial and error.. alot of it lol
possible rational roots?
last# ----- helps to narrow it down fisrt#
Rational root test, fundamental theorem of algebra, synthetic division
make a fraction, numerator must divide 5, denom must divide 1, so only choices are \[\pm1, \pm 5\]
no, not all the roots; but the integer and rational roots that could be determined from this lol
i know i am being silly. you meant to find possible rational roots.
how do you find the real roots?
might be able to work it inside out and complete squares to find all roots .... i wonder
there is no algorithm for finding the roots of a poly of degree seven.
only 1 - 4. that is it. and the one for 3 is a page and the one for 4 is a wall.
well, you could do the Newton Rhapsody method to find 1 root and narrow it down ..... perhaps ?
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 \[f(1)=1+3-5-2-5\]
make sure you include your zero place holders
well we have to find one first.
if you have a decent calculator check \[f(5)\]
syntheitc can find them as well; but brute calculating is always a good option lol
ok i will divide see if i get 0
Newton-Rhapsody :D :D
newton rhapsody in blue
5 doesn't work
and neither does -5 unless i made a mistake
-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
D's sign change tells us what ...... do we include zeros as a sign change?