6. Let ao, a1, a2, a3, a4 be constant real numbers such that a1 a2 a3 + + + + a4 = 0. 5 4 3 2 Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between 0 and 1. (Hint: Consider a1 4 a2 5 a3 f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² + Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in [0, 1]).

6. Let ao, a1, a2, a3, a4 be constant real numbers such that a1 a2 a3 + + + + a4 = 0. 5 4 3 2 Show that the polynomial P(x) = ax² + a₁x³ + a₂x² +a3x+a4 has at least one zero between 0 and 1. (Hint: Consider a1 4 a2 5 a3 f(x) = 2x³ + 2/1x²¹ +23²x³² +22³x² + Show that Rolle's theorem applies to f(x) on the interval [0, 1]. Deduce that P(x) has a 0 in [0, 1]).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 18RE

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