Kunze Linear Algebra · Problem 4.3.2

Polynomials

Mathematics — Methods · lagrange-interpolation-existence-condition

Problem

Let

\alpha, \beta, \gamma, \delta

be real numbers. We ask when it is possible to find a polynomial

f

over

R

, of degree not more than

2

, such that

f(-1) = \alpha

f(1) = \beta

f(3) = \gamma

and

f(0) = \delta

. Prove that this is possible if and only if

3\alpha + 6\beta - \gamma - 8\delta = 0.