If zero is obtained when a number is substituted for the variable in a polynomial, then that number is a root of the polynomial. For example, 1 is a root of x2 - 1.
Note A number r is a root of a polynomial if and only if x - r is a factor of that polynomial.
The factorization
dtbpFU2.9992in1.9995in0pt
y = x3 - x2 -
x + 2Plot
The preceding graph was created within Scientific Notebook. Click hereDM6.tex for the chapter discussing techniques for such displays.
The factorization
You can find all real and complex roots directly by applying Roots from the Polynomials menu.
To find the roots of a polynomial
Polynomials + Roots
x3 -ix2 -8x2 +
ix +
x + 6i -
, roots:
- i
5 + 3i 3
It follows from the Fundamental Theorem of Algebra that the number of roots (including complex roots and multiplicities) is the same as the degree of the polynomial.
For polynomials with rational (real or complex) coefficients, Scientific Notebook uses the usual formulas for finding roots symbolically for polynomials of degree 4 or less, and it finds the roots numerically for polynomials of higher degree. This behavior is due to the mathematical phenomenon that there is no general formula in terms of radical expressions for the roots of polynomials of degree 5 and higher.