GATE 2026 MN – Question 37
Data are (x,y)=(2,3),(2.5,3.5),(3,5). Newton’s polynomial is $y=b_0+b_1(x-2)+b_2(x-2)(x-2.5)$. Given b₀=3 and b₁=1, find b₂.
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Correct answer: (A) 2
Explanation
Insert the third data point:5=3+1(3−2)+b₂(3−2)(3−2.5). Hence5=4+0.5b₂, giving b₂=2, A. The unequal first divided differences generate the nonzero quadratic coefficient.