highskye1
contestada

Two roots of the polynomial function f(x) = x3 − 7x − 6 are −2 and 3. Use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). Explain your thinking.

Respuesta :

nunyabiznaz69ozr3z8

Answer: The degree of the polynomial is 3.

By the fundamental theorem of algebra, the function has three roots.

Two roots are given, so there must be one root remaining.

By the complex conjugate theorem, imaginary roots come in pairs.

The final root must be real.


Step-by-step explanation:

( x³ - 7 x - 6 ) : ( x + 2 ) = x² - 2 x - 3

-x³ - 2 x²

------------

     - 2 x² - 7 x

        2 x² +4 x

       --------------

                - 3 x - 6

                  3 x + 6

                 ------------

                  R(x) = 0

The polynomial: x³ - 7 x - 6  =  ( x + 2) ( x² - 2 x - 3  )

x² - 2 x - 3 = x² - 3 x + x - 3 = x ( x - 3 ) + ( x - 3 ) = ( x + 1 ) ( x - 3 )

The polynomial has roots : -2, 1, 3.

mattchewxfoxy

Answer:

The degree of the polynomial is 3.  By the fundamental theorem of algebra, the function has three roots.   Two roots are given, so there must be one root remaining.  By the complex conjugate theorem, imaginary roots come in pairs.  The final root must be real.

Step-by-step explanation: got it right on edge (: hope it helps! <3

Otras preguntas