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Find the smallest positive root of \( x^3 – 2x + 1 = 0 \) with relative accuracy of \( 0.5 \% \) by finding good starting value from its graph. According to the graph above, there are three roots, one negative and two positive. Let’s give \( f(x) = x^3-2x+1 \), then \( f(1) […]
Determin how many of the roots (zeroes) of a cubic polynomial are real by the use of the sums and products of a polynomial.
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 \( nM \ge |a_{n}| + |a_{n-1}| + |a_{n-2}| + \cdots + |a_2| + |a_1| \). […]