# Math

how many roots does this polynomial have: f(x) = 5x^3 + 8x^2 -4x + 3

and

Of the possible rational roots, which ones are roots: ±1, ±(1/5), ±3, ± (3/5)

1. 👍
2. 👎
3. 👁
1. According to the Fundamental Theorem of Algebra,
5x^3 + 8x^2 -4x + 3 =0 will have 3 roots, at least one of which must be real.
testing for x = 1
5 + 8 - 4 + 3 ≠ 0
testing for x = -1
-5 + 8 + 4 - 3 ≠ 0

tried the others, none worked, did not test the complex ones
Then tried Wolfram, go this
http://www.wolframalpha.com/input/?i=solve+5x%5E3+%2B+8x%5E2+-4x+%2B+3+%3D0

1. 👍
2. 👎

## Similar Questions

1. ### Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

2. ### POLYNOMIALS

The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did:

3. ### Math

Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots

4. ### algebra

How can you quickly determine the number of roots a polynomial will have by looking at the equation?

1. ### Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the

2. ### Math ( Pre Calc)

Find all real and imaginary roots of the polynomial equation 3x^4-x^3+4x^2-2x-4=0

3. ### Polynomials

Can you find the fourth degree polynomial with integer coefficients that has given roots for 2i and 4-i

4. ### Calculus

Suppose that ax^2 + bx + c is a quadratic polynomial and that the integration: Int 1/(ax^2 + bx + c) dx produces a function with neither a logarithmic or inverse tangent term. What does this tell you about the roots of the

1. ### math

how many real roots does the polynomial 2x^5+8x-7 have

2. ### Math

Determine the real roots of the polynomial equation: (x^2+1)(x-4)=0

3. ### Algebra

Solve the polynomial equation by finding all real roots x^4+15x^2-16 Many thanks

4. ### Algebra

A student claims that -4i is the only imaginary root of a quadratic polynomial equation that has real coefficients. a. What is the student’s mistake? (2 points) b. Write one possible polynomial that has the correct roots from