If -3 + i is a root of the polynomial function f(x), what can also be a root of f(x)?

Polynomials of degree n are linear combination of powers of a variable, i.e. they are the sum of all the powers of the variable from 0 to n, with some coefficients. So, a generic polynomial of degree n is written as

The fundamental theorem of algebra states that a polynomial of degree n has exactly n roots.

Moreover, polynomials with real coefficients also have the following property: if is a solution of a polynomial, its conjugate is also a solution of the same polynomial.

The conjugate is obtained by changing the sign of the complex part of the number:

So, if is a solution of the polynomial also its conjugate is a solution of the polynomial

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step-by-step explanation:

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