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Authors:
Anany Levitin
Chapter:
Coping With The Limitations Of Algorithm Power
Exercise:
12.4 Exercise
Question:3 | ISBN:9780132316811 | Edition: 3

Question

a.Prove that if p(x) is a polynomial of an odd degree, then it must have atleast one real root.

b.Prove that if x0 is a root of ann-degree polynomial p(x), the polynomialcan be factored into

                      p(x)=(x−x0)q(x),

where q(x) is a polynomial of degreen−1.Explain what significance thistheorem has for finding the roots of a polynomial.

c.Prove that if x0 is a root of ann-degree polynomialp(x),then

                      p′(x0)=q(x0),

where q(x) is the quotient of the division of p(x) by x−x0.

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