# Algebra 2:)

posted by .

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:) -

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

## Similar Questions

1. ### Math

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) 17x3 − x + 3 = x3 + 24x2 + x
2. ### ALGEBRA

Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.) x2 - 5x + 5 = 0 x = x =
3. ### ALGEBRA

Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.) x2 - 5x + 5 = 0 x = x =
4. ### Polynomials. :) :)

2x^4+4x^3-7x^2-x+7 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.
5. ### Polynomials. :) :)

f(x)=2x^4+4x^3-7x^2-x+7 has no rational roots. 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
6. ### ALGEBRA

Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.) 4x2 = 19x + 5 x = x =
7. ### Algebra

Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.) x2 - 5x + 5 = 0 x = x =
8. ### college algebra

Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) x4 + 27x = 0
9. ### algebra

solve the equation. Enter the answer as a comma-separated list. if there is no real solution, enter no real solution. x upper 2 - 10x+20=0
10. ### Trigonometry

Solve the equation, where 0° ≤ x < 360°. Round approximate solutions to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 3 sin x − 3 cos x = …

More Similar Questions