QJEEM21Maccf5: JEE Main 2021 Mathematics - Class 11 JEEM21Maccf5 Solution: Let f(x) be a polynomial of degree 3 such that f ( k ) = − 2 k…

Question

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Let f(x) be a polynomial of degree 3 such that

f (k) = - \frac{2}{k}

for k = 2, 3, 4, 5. Then the value of 52

-

10f(10) is equal to :

Accepted Answer

k f (k) + 2 = λ (x - 2) (x - 3) (x - 4) (x - 5)

.... (1)

put x = 0

we get

λ = \frac{1}{60}

Now, put

λ

in equation (1)

\Rightarrow k f (k) + 2 = \frac{1}{60} (x - 2) (x - 3) (x - 4) (x - 5)

Put x = 10

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

\Rightarrow 52 - 10 f (10) = 52 - 26 = 26

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