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 th
Question
2 Answer

1. User Answers 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.
Stepbystep 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.

2. User Answers 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.
Stepbystep explanation: got it right on edge (: hope it helps! <3