Let fx be a polynomial of degree 3 such that fk-2k for k - 2- 3- 4- 5- Then the value of 52 - 10 f10 is equal to

Let P(k) = kf(k) + 2 ⇒ kf(k) + 2 = a(x 2)(x 3)(x 4)(x 5) If k = 0 ⇒ 2 = a( 2)( 3)( 4)( 5) ∴ a=160 ⇒ kf(k)+2=160(x 2)(x 3)(x 4)(x 5) Putting k = 10 ⇒ 10f ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Descarte's Rule for Positive Roots

Let fx be a p...

Question

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 $52 - 10 f (10)$ is equal to

26.00

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

26.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

Let $P (k) = k f (k) + 2$
$\Rightarrow k f (k) + 2 = a (x - 2) (x - 3) (x - 4) (x - 5)$
If $k = 0$
$\Rightarrow 2 = a (- 2) (- 3) (- 4) (- 5)$
$∴ a = \frac{1}{60}$
$\Rightarrow k f (k) + 2 = \frac{1}{60} (x - 2) (x - 3) (x - 4) (x - 5)$
Putting $k = 10$
$\Rightarrow 10 f (10) + 2 = \frac{1}{60} \cdot 8 \cdot 7 \cdot 6 \cdot 5 = 28$
$∴ 10 f (10) = 26$
$\Rightarrow 52 - 10 f (10) = 26$

Suggest Corrections

Similar questions

Q. 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 - 10 f (10)

is equal to

Q. Let P(x) be a fourth degree polynomial with derivative P'(x). Such that

P (1) = P (2) = P (3) = P^{'} (7) = 0

. Let k is the real number such that

P (k) = 0

, then k is equal to

Q. Let p(x) be a polynomial of degree 4 such that p(k) =1/k for k=1,2,3,4,5 then 12 p(6) is equal to :

Q. If

f (x)

is a polynomial of degree

n (> 2)

and

f (x) = f (k - x), (

where

k

is a fixed real number

),

then degree of

f^{'} (x)

Q. Let

f : R \to R

be defined as

f (x + y) + f (x - y) = 2 f (x) f (y)

f (\frac{1}{2}) = - 1

. Then the value of

20 \sum k = 1 \frac{1}{sin (k) sin (k + f (k))}

is equal to

Join BYJU'S Learning Program

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

Let P(k)=kf(k)+2 ⇒kf(k)+2=a(x−2)(x−3)(x−4)(x−5) If k=0 ⇒2=a(−2)(−3)(−4)(−5) ∴a=160 ⇒kf(k)+2=160(x−2)(x−3)(x−4)(x−5) Putting k=10 ⇒10f(10)+2=160⋅8⋅7⋅6⋅5=28 ∴10f(10)=26 ⇒52−10f(10)=26

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 $52 - 10 f (10)$ is equal to