Given the following set S of polynomials, find a polynomial p(x) in P₂ so that SU {p(x)} spans P2 and a non-zero polynomial q(x) in P2 so that SU {q(x)} does not span P2. Use the '^' character to indicate an exponent, e.g. 5x^2-2x+1. S={−5x²+4x−9, −8x²−6x+8| p(x) = 0 q(x) = 0

Given the following set S of polynomials, find a polynomial p(x) in P₂ so that SU {p(x)} spans P2 and a non-zero polynomial q(x) in P2 so that SU {q(x)} does not span P2. Use the '^' character to indicate an exponent, e.g. 5x^2-2x+1. S={−5x²+4x−9, −8x²−6x+8| p(x) = 0 q(x) = 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 54E

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Question

Given the following set S of polynomials, find a polynomial p(x) in P2 so that SU {p(x)} spans P₂ and a non-zero polynomial q(x) in P2 so that SU{q(x)} does not span P2.
Use the '^' character to indicate an exponent, e.g. 5x^2–2x+1.
5-|-5x²+4x-9, −8x²-6x+8]
p(x) = 0 q(x) = 0

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