Posted by **Honey** on Thursday, May 17, 2012 at 10:40am.

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.

- Algebra 2:) -
**Steve**, Thursday, May 17, 2012 at 11:21am
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

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