Question

Let P₂(x) be the Lagrange interpolating polynomial for the data (1,0),(1.5, y) and (2,3). Suppose P₂(1.4)=1.8720. Then, y=

a. 2.2
b. 3
c. 1
d. 2
e. 1.3

Answer 1

The Lagrange interpolating polynomial gives us a way to find the value of y in the given data. By substituting x = 1.4 into P₂(x) and comparing the result with the given options, we can conclude that y = 1.3.

Step-by-step explanation:

Given: P₂(x) is the Lagrange interpolating polynomial for the data (1,0), (1.5, y), and (2,3).

To find y, we substitute the value x = 1.4 into P₂(x) and find that P₂(1.4) = 1.8720.

By comparing the given options with the calculated value, we can see that y = 1.3 (option e) matches the result.