GATE 2022 MA – Question 30
P is a degree-5 polynomial and x₀,…,x₆ are distinct in [2,3]. Let $\alpha=\sum_{i=0}^6P(x_i)\prod_{j\ne i}(x_i-x_j)^{-1}$. Find α²−α+1.
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Correct answer: 1 to 1
Explanation
In the seven-node Lagrange interpolant the displayed sum is the coefficient of x⁶. The interpolant equals P, whose degree is 5, so this coefficient α is zero. Hence **α²−α+1=1**.