f(x)=x^5-2x^4-2x^3+4x^2-3x+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