Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : p2(x) = 3 +1/2(x−a) + b(x−a)(x−3/2). Now, the scientist wants to do more experiment and got one more point (2,5/3) Therefore, the total data is the following. x 1 3/2 0 2 y 3 13/4 3 5/3 Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial p3(x) = c + d(x−1) + (1/3)(x−1)(x−3/2) + e(x−1)(x−3/2)x. Then, answer as an integer or fractional expression (for example, 1/2)

In an experiment, a scientist obtained the following data. 

Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : p₂(x) = 3 +1/2(x−a) + b(x−a)(x−3/2).

Now, the scientist wants to do more experiment and got one more point (2,5/3)

Therefore, the total data is the following.

Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial

p₃(x) = c + d(x−1) + (1/3)(x−1)(x−3/2) + e(x−1)(x−3/2)x.

Then, answer as an integer or fractional expression (for example, 1/2)

a =  

b =  

c =  

d =  

e =