Find the sum of the three coefficient polynomials, Engineering Mathematics

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Find the quadratic that interpolates f(x) = 2x3 - x + 1 at the nodes x0 = 0, x1 = 2, x2 = 3,

a) by solving a set of three equations for the coefficients of p2(x) = a2x2 + a1x + a0.

b) by using Lagrange's approach.

From b) find the sum of the three coefficient polynomials lk(x), k = 0, 1, 2.


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