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

1. amistre64

trial and error.. alot of it lol

2. anonymous

possible rational roots?

3. amistre64

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

4. anonymous

Rational root test, fundamental theorem of algebra, synthetic division

5. amistre64

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

6. anonymous

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

7. 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.

8. amistre64

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

9. anonymous

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

10. anonymous

how do you find the real roots?

11. amistre64

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

12. anonymous

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

13. anonymous

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

14. amistre64

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

15. 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 $f(1)=1+3-5-2-5$

16. amistre64

make sure you include your zero place holders

17. anonymous

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

18. anonymous

well we have to find one first.

19. anonymous

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

20. amistre64

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

21. anonymous

ok i will divide see if i get 0

22. watchmath

Newton-Rhapsody :D :D

23. anonymous

newton rhapsody in blue

24. anonymous

5 doesn't work

25. anonymous

and neither does -5 unless i made a mistake

26. 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

27. amistre64

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