What is the real root of x^5+5x^3+5x-1?

eddybob123 · 2013-08-22T00:47:21+00:00

Find the real root of x^5+5x^3+5x-1

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Thread starter eddybob123
Start date Aug 21, 2013
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Polynomial Root

In summary, to find the root of a polynomial, there are several methods that can be used such as the rational root theorem, synthetic division, or the quadratic formula. The rational root theorem helps to find possible rational roots by using the factors of the constant term and leading coefficient. Synthetic division is most useful for polynomials with a degree of three or higher, as it simplifies long division. The quadratic formula can only be used for quadratic polynomials, and for higher degree polynomials, other methods such as the rational root theorem or synthetic division should be used. In some cases, a polynomial may have no real roots, and the discriminant can be used to determine if the roots are imaginary or if there are no roots at all.

Aug 21, 2013

eddybob123

Find the real root of $\displaystyle x^5+5x^3+5x-1$

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Aug 22, 2013

eddybob123

Hint:
[sp]Let $\displaystyle x=u+\frac{k}{u}.$[/sp]

Related to What is the real root of x^5+5x^3+5x-1?

1. How do I find the root of a polynomial?

To find the root of a polynomial, you can use a variety of methods such as the rational root theorem, synthetic division, or the quadratic formula. These methods involve manipulating the polynomial equation and solving for the variable that makes the equation equal to zero.

2. What is the rational root theorem?

The rational root theorem is a method used to find possible rational roots of a polynomial. It states that if a polynomial has rational roots, they can be expressed as a fraction where the numerator is a factor of the constant term and the denominator is a factor of the leading coefficient.

3. When should I use synthetic division to find the root of a polynomial?

Synthetic division is most useful when trying to find the roots of a polynomial with a degree of three or higher. It simplifies the process of long division and allows you to quickly test potential roots to see if they are valid.

4. Can I use the quadratic formula to find the root of any polynomial?

No, the quadratic formula can only be used to find the roots of a quadratic polynomial, which has a degree of two. For polynomials with a higher degree, you will need to use other methods such as the rational root theorem or synthetic division.

5. What if I cannot find the root of a polynomial?

If you are unable to find the root of a polynomial, it is possible that the polynomial has no real roots. In this case, you can use the discriminant to determine whether the polynomial has imaginary roots or no roots at all.