GATE 2020 MA – Question 30
For f(x) = x⁴, let p be its interpolating polynomial at nodes 1,2,3. Find p(0).
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Show answer and explanation
Correct answer: 36 to 36
Explanation
The Lagrange basis values at zero are $L_1(0)=3$, $L_2(0)=-3$ and $L_3(0)=1$. Thus $p(0)=f(1)(3)+f(2)(-3)+f(3)(1)=3-48+81=36$. The polynomial has degree at most two because there are three interpolation nodes.