how do you find the rational and real roots?

x^7+3x^6-5x^2-3x-5=0

Question

how do you find the rational and real roots?

x^7+3x^6-5x^2-3x-5=0

amistre64 · Answer

trial and error.. alot of it lol

anonymous · Answer

possible rational roots?

amistre64 · Answer

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

anonymous · Answer

Rational root test, fundamental theorem of algebra, synthetic division

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

how do you find the real roots?

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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 · Answer

make sure you include your zero place holders

anonymous · Answer

$$f(-1)=-1+3-5+3-5=-1$$

anonymous · Answer

well we have to find one first.

anonymous · Answer

if you have a decent calculator check $$f(5)$$

amistre64 · Answer

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

anonymous · Answer

ok i will divide see if i get 0

watchmath · Answer

Newton-Rhapsody :D :D

anonymous · Answer

newton rhapsody in blue

anonymous · Answer

5 doesn't work

anonymous · Answer

and neither does -5 unless i made a mistake

amistre64 · Answer

-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 · Answer

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