Civil Engineering > GATE 2026 SET-1 > Numerical Methods
Values of y for different values of x are tabulated below.
If a second-degree interpolating polynomial P2(x) is used to represent y, the value of P2(0) is ___________ (rounded off to the nearest integer).
Correct : 2
Using the three data points (−2, 28), (1, 4), (2, 16), a second-degree polynomial P₂(x) = ax² + bx + c is fitted.
Setting up the three equations:
4a − 2b + c = 28 ... (i)
a + b + c = 4 ... (ii)
4a + 2b + c = 16 ... (iii)
Subtracting (ii) from (iii): 3a + b = 12 ... (iv)
Subtracting (ii) from (i): 3a − 3b = 24 → a − b = 8 ... (v)
Adding (iv) and (v): 4a = 20 → a = 5
From (v): b = 5 − 8 = −3
From (ii): c = 4 − 5 + 3 = 2
So P₂(x) = 5x² − 3x + 2
P₂(0) = 5(0)² − 3(0) + 2 = 2
Correct answer: 2
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