16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.3.2

Polynomials

Mathematics — Linear Algebra · lagrange-interpolation-condition

Problem

Let α,β,γ,δ\alpha, \beta, \gamma, \delta be real numbers. We ask when it is possible to find a polynomial ff over RR, of degree not more than 22, such that f(−1)=αf(-1) = \alpha, f(1)=βf(1) = \beta, f(3)=γf(3) = \gamma and f(0)=δf(0) = \delta. Prove that this is possible if and only if 3α+6β−γ−8δ=0.3\alpha + 6\beta - \gamma - 8\delta = 0.

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