Question

Let f(x) be a polynomial of degree 3 such that f(k) = -(2/k) for k = 2, 3, 4, 5. Then the value of 52 – 10 f(10) is equal to :

Answer 1

k f(k) + 2 = l (x – 2) (x –3) (x – 4) (x – 5) …(1) 

put x = 0

we get λ = \(\frac{1}{60}\) 

Now,

Put λ in equation (1)

⇒ kf(k) + 2 = \(\frac{1}{60}\) (x – 2) (x – 3) (x – 4) (x – 5)

Put x = 10

⇒ 10f(10) + 2 = \(\frac{1}{60}\)(8) (7) (6) (5)

⇒ 52 – 10f(10) = 52 – 26 = 26