Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (2, 1), (3, 1), (4, −3), (5, 0).

cistG 2020-10-28 Answered
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (2, 1), (3, 1), (4, 3), (5, 0).
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Expert Answer

hajavaF
Answered 2020-10-29 Author has 90 answers
Step 1 With x1=2, x2=3, and x4=5, the Langrange interpolating polynomials give: p1(x)= (x  x2){x  x3)(x  x4)(x1  x2)(x1  x3)(x1  x4)
= (x  3)(x  4)(x  5)(2  3)(2  4)(2  5)
= (x2  7x + 12)(x  5)(1)(2)(3)
=  x3  5x2  7x2 + 35x + 12x  606
=  16x3 + 2x2  476x + 10
p2(x)= (x  x1)(x  x3)(x  x4)(x2  x1)(x2  x3)(x2  x4)
= (x  2)(x  4)(x  5)(3  2)(3  4)(3  5)
= (x2  6x + 8)(x  5)(1(1)(2))
= x3  11x2 + 38x  402
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