Algebra 2:)
posted by Honey on .
f(x)=x^52x^42x^3+4x^23x+3
Approximate the irrational solutions correct to 3 decimals. If there is more than 1 real solution, enter them from smallest to largest, separated by a comma.

a little synthetic division shows that all the real roots are between 2 and 3.
Descartes' Rule of Signs shows that there are at most
3 positive roots
1 negative root
Since complex roots appear in pairs, if there's one negative root, there can only be 2 positive roots.
So, try bisection
f(2) = 23
f(1) = 9
f(1.5) = 5.5
f(1.75) = 3.9
f(1.625) = 1.743
f(1.6875) = 0.839
f(1.65625) = 0.515
f(1.671875) = 0.146
and so on till you get f(1.6685) = 0
proceed likewise for the other roots.
1.668, 1.208, 2.244