Question

Find a second-degree polynomial p such that p(1) = 5, p'(1) = 3, and p''(1) = 6.

Answer 1

let polynomial be ax.x + bx + c

p(1) = a + b+ c = 5

p'(x) = 2ax + b
p'(1)= 2A + B = 3

P''(x) = 2a = 6

a=3





b = -3

c = 5
hence polynomial is 3 x.x -3x + 5