Question

How many solutions over the complex number system does this polynomial have?
3x6 – x3 - 4x2 + 3x + 52 = 0
Enter your answer as an integer. Can somebody plzzzzzzzzz help me plzzzzzzzz I really need help with this plzzzzzzz can anyone help??????????

Answer 1

Answer:

6 complex numbers

Answer 2

There are 6 solutions to the polynomial over the complex number system.

The given equation is 3$x^{6}$-x³-4x²+5x+52=0.

What is the complex number system of a polynomial?

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system. A further theorem, in some cases referred to as the Linear Factorization Theorem, states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c), where c is a root. These n complex roots are counted with multiplicity.

In polynomials, the number of roots or highest power is equal to the degree of the polynomial.

Here, 3$x^{6}$-x³-4x²+5x+52=0.

We can see that the polynomial is a sixth-degree polynomial.

Therefore, there are 6 solutions to the polynomial over the complex number system.

Learn more about polynomials here:

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