Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation: a+b/2+c/3+d/4 = 0 show that the equation p(x) = 0 has a root between 0 and 1. Can you generalize this result for an nth-degree polynomial?
Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation: a+b/2+c/3+d/4 = 0 show that the equation p(x) = 0 has a root between 0 and 1. Can you generalize this result for an nth-degree polynomial?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Complex Numbers
Section4.2: Complex Solutions Of Equations
Problem 7ECP: Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.
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Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation: a+b/2+c/3+d/4 = 0
show that the equation p(x) = 0 has a root between 0 and 1. Can you generalize this result for an nth-degree polynomial?
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