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## What is complex roots of polynomials?

In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

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How do you find the roots of a polynomial?

You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2×4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.

Do all polynomials have complex roots?

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system (keep in mind that a complex number can be real if the imaginary part of the complex root is zero).

### How do you find the roots by Factorisation?

The roots of the quadratic equation by the method of the factorization for (i) x² – 3x -10 = 0 (ii) 2x² + x – 6 = 0 (iii) √2x² + 7x + 5√2 = 0 (iv) 2x² – x + 1/ 8 = 0 (v) 100x² – 20x + 1= 0 are (i) – 2, 5, (ii) 3/2, -2, (iii) – 5/√2, – √2, (iv) 1/4, 1/4 and (v) 1/10, 1/10 respectively.

What is a root of polynomial?

What are the roots of a polynomial? Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero. If a is the root of the polynomial p(x), then p(a) = 0.

How do you factor a polynomial with a complex root?

A simplified version of the LLL factorization algorithm is as follows: calculate a complex (or p -adic) root α of the polynomial . One can determine a bound for the precision that guarantees that this method produces either a factor, or an irreducibility proof.

#### What is polynomial factorization?

Polynomial factorization is one of the fundamental components of computer algebra systems. The first polynomial factorization algorithm was published by Theodor von Schubert in 1793. Leopold Kronecker rediscovered Schubert’s algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.

When was the first polynomial factorization algorithm invented?

The first polynomial factorization algorithm was published by Theodor von Schubert in 1793. Leopold Kronecker rediscovered Schubert’s algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension. But most of the knowledge on this topic is not older than circa 1965 and the first computer algebra systems :

What is Knuth’s book on factorization of polynomials?

Knuth, Donald E (1997). “4.6.2 Factorization of Polynomials”. Seminumerical Algorithms. The Art of Computer Programming. 2 (Third ed.).