Question

find the second degree polynomial with P(0)=3, P(1)=6, P(-1)=2

Answer 1

Answer:

required polynomial is x^2 + 2x + 3

Step-by-step explanation:

Let the polynomial be p(x) = ax^2 + b x + c

p(0) = c = 3

p(1) = a + b + c = 6

⇒ a + b + 3 = 6

⇒ a + b = 3 → (1)

p(-1) = a - b + c = 2

⇒ a - b + 3 = 2

⇒ a - b = -1 → (2)

(1) + (2) ,

2a = 2

⇒ a = 1

∴ b = 2

required polynomial is x^2 + 2x + 3