# How many complex roots can a polynomial have?

## How many complex roots can a polynomial have?

The fundamental theorem of algebra says that every polynomial function has at least one root in the complex number system.

### What are 2 complex roots?

A given quadratic equation ax2 + bx + c = 0 in which b2 -4ac < 0 has two complex roots: x = , . Therefore, whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial.

What are complex roots in a polynomial?

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.

Does every polynomial have complex roots?

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.

## Is under root 2x a polynomial?

Step-by-step explanation:^2*-1 CAN BE WRITTEN AS ^2*1/2*-1. HERE THE EXPONENT OF 2 IS 1/2,WHICH IS NOT A WHOLE NUMBER.SO,IT IS NOT A POLYNOMIAL.

### What is complex root?

complex rootA complex root is a complex number that, when used as an input ( ) value of a function, results in an output ( ) value of zero. Imaginary NumbersAn imaginary number is a number that can be written as the product of a real number and .

Why are complex roots in pairs?

From a more technical point of view, the reason complex numbers come in pairs is that there are precisely two field automorphisms of the complex numbers that leave the real numbers in place. One of the these is the identity function on C, and the other is conjugation (a+bi -> a-bi).

How do you write polynomial from its roots?

Write a polynomial from its roots : Root is nothing but the value of the variable that we find in the equation.To get a equation from its roots, first we have to convert the roots as factors. By multiplying those factors we will get the required polynomial. 2 and 3 are the roots of the polynomial then we have to write it as x = 2 and x = 3.

## How do you calculate polynomials?

Calculating the volume of polynomials involves the standard equation for solving volumes, and basic algebraic arithmetic involving the first outer inner last (FOIL) method. Write down the basic volume formula, which is volume=length_width_height. Plug the polynomials into the volume formula. Example: (3x+2)(x+3)(3x^2-2)

### What is the conjugate pair theorem?

Conjugate Pair Theorem An assertion about the complex zeros of any polynomial which has real numbers as coefficients. Theorem: If a polynomial p ( x) = a n x n + a n –1x n – 1 + ··· + a 2 x 2 + a 1 x + a 0 has real coefficients, then any complex zeros occur in conjugate pairs.

What is a factor polynomial?

Factorization of a Polynomial. A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x 2 – 4. The factorization of a polynomial is its representation as a product its factors. For example, the factorization of x 2 – 4 is (x – 2)(x + 2).