f,(x) = x, f,(x) = x - 1, f,(x) = x + 6 g(x) = c,f,(x) + czf2(x) + C3f3(x) Solve for c,, C, and c, so that g(x) 0 on the interval (-o, co). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution %3D (G, ) - {0,0,0x} {c, C2. C3} = { 0, 0, 0

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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Consider the following functions.
f,(x) = x, f,(x) = x - 1, f,(x) =
g(x) = c,f,(x) + c2f2(x) + czf3(x)
x + 6
Solve for c,, c,, and c, so that g(x) = 0 on the interval (-o, 0). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
{C1, C2, C3} = { 0, 0, 0
Transcribed Image Text:Consider the following functions. f,(x) = x, f,(x) = x - 1, f,(x) = g(x) = c,f,(x) + c2f2(x) + czf3(x) x + 6 Solve for c,, c,, and c, so that g(x) = 0 on the interval (-o, 0). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C1, C2, C3} = { 0, 0, 0
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