perplexus.info :: Just Math : Interpolating Polynomial

Interpolating Polynomial (Posted on 2025-01-12)

Let f(x) be a monic 4th degree polynomial such that f(1) = 1, f(2) = 8, f(3) = 27, f(4) = 64. Find f(5).

No Solution Yet Submitted by Danish Ahmed Khan

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Computer solution

| Comment 2 of 3 |

f(x) = x^4 + ax^3 + bx^2 + cx + d

1 + a + b + c + d = 1

16 + 8a + 4b + 2c + d = 8

81 + 27a + 9b + 3c + d = 27

256 + 64a + 16b + 4c + d = 64

Solution of simultaneous equations

(it turns out python has such a function in the sympy library)

{a: -9, b: 35, c: -50, d: 24}

f(x) = x^4 - 9x^3 + 35x^2 - 50x + 24

x f(x)

0 24

1 1

2 8

3 27

4 64

5 149

f(5) = 149

Posted by Larry on 2025-01-12 08:54:17

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