Determin how many of the roots (zeroes) of a cubic polynomial are real by the use of the sums and products of a polynomial.
Polynomials
Polynomial Equations and Maximum Coefficients
If \( \alpha \) is a root of a polynomial equation \( P(x) = 0 \), then \( P(\alpha) = 0 \), and if \(M\) is the maximum coefficient value of \( |a_{n}|, |a_{n-1}|, |a_{n-2}|, \cdots ,|a_2|, |a_1| \) then \( nM \ge |a_{n}| + |a_{n-1}| + |a_{n-2}| + \cdots + |a_2| + |a_1| \). […]