︠dfe3f173-5639-4d26-b247-2a8b255b25a0︠
x = var('x');
poly = x^5 - 5*x^4 - 67*x^3 + 257*x^2 + 822*x - 800
︠a939a0ae-2f5e-4723-b7cd-c4c3abe1c6d6︠
plot(poly, (x, -7.2, 8.2))
︠c15144eb-a1d9-44a9-9d52-25d5c88eb8c2︠
# Can't be solved because there is no general formula for polynomials of degree 5
# See http://en.wikipedia.org/wiki/Insolubility_of_the_quintic
solve(poly==0, x)
︠8651810c-0b12-4abf-8b13-54814c0e7fd8︠
# We can solve it with find_root  We need to give find_root a range and it will
# find a root in the range.  So to find all the roots we need to call find_root
# multiple times.  Here we can look at the plot to find ranges.

# Here is an approximation to the rightmost root
find_root(poly, 7, 8.5)
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find_root(poly, -4, -2)
︠67981aed-af08-44a8-ba5c-6545b68321d8︠
# If we give a range where there is no root, we get an error
find_root(poly, 10, 20)
︠45422a75-5733-43fd-8c81-56fe1d7df010︠