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 – 10f(10) is equal to ______.

Options

• 25

• 26

• 27

• 28

Answer 1

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 – 10f(10) is equal to 26.

Explanation:

Let k f(k)+ 2 = λ(k – 2) (k – 3) (k – 4) (k – 5)  ...(i)

Put k = 0

We get λ = `1/60`

Now, put λ in equation (i)

⇒ kf(k) + 2 = `1/60(k - 2)(k - 3)(k - 4)(k - 5)`

Put k = 10

⇒ 10f(10) + 2 = `1/60(8)(7)(6)(5)` = 28

⇒ 10f(10) = 26

⇒ 52 – 10f(10) = 52 – 26 = 26