Days 8 and 9: Using the Fundamental Theorem of Algebra
To wrap it in a nutshell, the fundamental theorem of algebra guarantees the following to us:
A polynomial function of degree n will have n roots (cubics have 3 roots, quartics have 4 roots, etc.)
Furthermore, polynomials of an even degree will have a minimum of 0 real roots (yes, it is possible for a quartic to have four complex roots, 2 pairs of complex conjugates)
Also, polynomials of an odd degree will have a minimum of 1 real root (so, a cubic may have 1 real root and one pair of complex conjugates)
To wrap it in a nutshell, the fundamental theorem of algebra guarantees the following to us:
A polynomial function of degree n will have n roots (cubics have 3 roots, quartics have 4 roots, etc.)
Furthermore, polynomials of an even degree will have a minimum of 0 real roots (yes, it is possible for a quartic to have four complex roots, 2 pairs of complex conjugates)
Also, polynomials of an odd degree will have a minimum of 1 real root (so, a cubic may have 1 real root and one pair of complex conjugates)
« Prev Page
Next Page »
