GATE 2021 MA – Question 32

Numerical Analysis · Interpolation · 1 mark · Numerical answer

A cubic p(x)=α+β(x+2)+γ(x+2)(x+1)+δ(x+2)(x+1)x interpolates values at x=(−2,−1,0,1,2) of (2,−1,8,5,−34). Find α+β+γ+δ.

Show answer and explanation

Correct answer: 1 to 1

Explanation

Successively substitute −2,−1,0,1: α=2,β=−3,γ=6,δ=−4. At x=2 this gives 2−12+72−96=−34, confirming the fifth datum. Sum=2−3+6−4=**1**.

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