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Find the quadratic that interpolates f(x) = 2x^{3} - x + 1 at the nodes x_{0} = 0, x_{1} = 2, x_{2} = 3,
a) by solving a set of three equations for the coefficients of p_{2}(x) = a_{2}x^{2} + a_{1}x + a_{0}.
b) by using Lagrange's approach.
From b) find the sum of the three coefficient polynomials l_{k}(x), k = 0, 1, 2.
basic properties on the inverse of laplace transform
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