Question

True or false15. Complex roots of polynomials with real coefficients always occur as conjugate pairs

Answer 1

The theorem named "Complex Conjugate Root Theorem" states that if you have a complex root of a polynomial in one variable with real coefficients,

`x=a+bi`

then, its conjugate,

`x^*=a-bi`

is also a root to the same polynomial.

So, it is True that complex roots of polynomials os real coefficients always occur as conjugate pais:

`\begin{gathered} x=a_{}+bi \\ x^*=a-bi \end{gathered}`