Find a second-degree polynomial P such that P(1) = 5, P'(1) = 8, and P''(1) = 10.

Question

Find a second-degree polynomial P such that P (1) = 5, P'(1) = 8, and P''(1) = 10.

Thank you.

Answer 1

Assume a second degree polynomial is

p(x) =a x² + b x + c .......1

p(1) = 5 , plug 1 for x in eq. 1

a + b + c = 5 .........2

p' (x) = 2a x + b

p'(1) = 8

2a + b = 8 ........3

p'' (x) = 2a

p''(1) = 10

2a = 10

a = 5

plug a=5 in eq. 3

10 + b = 8

b = -2

plug a= 5 and b = - 2 in eq.2

5 - 2 + c = 5

c = 2

so , the second degree polynomial is :

p(x) = 5 x² -2 x + 2