Let P₂(x) = {ax² + b | a, b e R and a #0}. If p(x) = ax² +b and g(x) = cx² + d are elements of P2(x), let be the operation on P₂ such that. Show that (P2, p(x) * q(x) = (ac) x² + (ad + bc) (P2, *) is a group.
Let P₂(x) = {ax² + b | a, b e R and a #0}. If p(x) = ax² +b and g(x) = cx² + d are elements of P2(x), let be the operation on P₂ such that. Show that (P2, p(x) * q(x) = (ac) x² + (ad + bc) (P2, *) is a group.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let P₂(x) = {ax² + b | a, b E R and a #0}. If
p(x) = ax
= ax² +b and g(x) = cx² + d are elements of P₂(x),
let ✩ be the operation on P₂ such that.
Show that P2, is a group.
★
p(x) *q(x) = (ac)x² + (ad + bc)
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