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12. (a) For n = 3, explain why Lo(x)+ L1(x) + L2(x)+L3(x) = 1 for all x. Hint: It is unnecessary to actually multiply out and combine the functions L;(x) of (4.14). Use (4.13) with a suitable choice of {yo, Yı1, Y2, y3}. (b) Generalize part (a) to an arbitrary degree n > 0.

12. (a) For n = 3, explain why Lo(x)+ L1(x) + L2(x)+L3(x) = 1 for all x. Hint: It is unnecessary to actually multiply out and combine the functions L;(x) of (4.14). Use (4.13) with a suitable choice of {yo, Yı1, Y2, y3}. (b) Generalize part (a) to an arbitrary degree n > 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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12. (a) For n = 3, explain why Lo(x) + L1(x) + L2(x) +L3(x) = 1 for all x. Hint: It is unnecessary to actually multiply out and combine the functions L;(x) of (4.14). Use (4.13) with a suitable choice of {yo, y1, y2, y3}. (b) Generalize part (a) to an arbitrary degree n > 0.
Transcribed Image Text:12. (a) For n = 3, explain why Lo(x) + L1(x) + L2(x) +L3(x) = 1 for all x. Hint: It is unnecessary to actually multiply out and combine the functions L;(x) of (4.14). Use (4.13) with a suitable choice of {yo, y1, y2, y3}. (b) Generalize part (a) to an arbitrary degree n > 0.
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