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

Answer :

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

[tex]x=a+bi[/tex]

then, its conjugate,

[tex]x^*=a-bi[/tex]

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:

[tex]\begin{gathered} x=a_{}+bi \\ x^*=a-bi \end{gathered}[/tex]