how do you find the rational and real roots?
x^7+3x^6-5x^2-3x-5=0

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- anonymous

how do you find the rational and real roots?
x^7+3x^6-5x^2-3x-5=0

- schrodinger

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- amistre64

trial and error.. alot of it lol

- anonymous

possible rational roots?

- amistre64

last#
----- helps to narrow it down
fisrt#

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## More answers

- anonymous

Rational root test, fundamental theorem of algebra, synthetic division

- amistre64

i was thinking of writing a javascript to solve these things ;)

- anonymous

make a fraction, numerator must divide 5, denom must divide 1, so only choices are
\[\pm1, \pm 5\]

- 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

no, not all the roots; but the integer and rational roots that could be determined from this lol

- anonymous

i know i am being silly. you meant to find possible rational roots.

- anonymous

how do you find the real roots?

- amistre64

might be able to work it inside out and complete squares to find all roots .... i wonder

- anonymous

there is no algorithm for finding the roots of a poly of degree seven.

- anonymous

only 1 - 4. that is it. and the one for 3 is a page and the one for 4 is a wall.

- amistre64

well, you could do the Newton Rhapsody method to find 1 root and narrow it down ..... perhaps ?

- 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

make sure you include your zero place holders

- anonymous

\[f(-1)=-1+3-5+3-5=-1\]

- anonymous

well we have to find one first.

- anonymous

if you have a decent calculator check \[f(5)\]

- amistre64

syntheitc can find them as well; but brute calculating is always a good option lol

- anonymous

ok i will divide see if i get 0

- watchmath

Newton-Rhapsody :D :D

- anonymous

newton rhapsody in blue

- anonymous

5 doesn't work

- anonymous

and neither does -5 unless i made a mistake

- 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

D's sign change tells us what ...... do we include zeros as a sign change?

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