 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/ib/paper-3/19d/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

0, 2, 3

gives

a (x) = \frac{( x - 2 ) ( x - 3 )}{6}, b (x) = - \frac{x ( x - 3 )}{2}, c (x) = \frac{x ( x - 2 )}{3} .

Each polynomial is one at its own node and zero at the other two. For a polynomial

f

of degree at most two, the difference between

f

and this interpolation polynomial has degree at most two and three distinct roots, so it is identically zero. This also proves uniqueness of the quadratic coefficients.

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