Question

Let P(x) be a polynomial of degree 5 such that P(k)= 3^k for k=0,1,2,3,4,5. Then the sum of the digit in
P(6) is?​

Answer 1

Answer:

The sum of digit in 729 = 7 + 2 + 9 = 18.

Step-by-step explanation:

As we know  that

P(k) = 3^k

Hence , now for  P(6)

P(6) = 3^6

P(6) = 729

Thus sum of digit in 729 = 7+2+9 = 18

Answer 2

Sum of digits in P(6) is 18.

Step-by-step explanation:

The polynomial given of degree 5 such that $P(k)= 3^k$ for k=0,1,2,3,4,5.

We have to find the sum of the digit in  P(6).

Now,  $P(k)= 3^k$

$P(k)-3^k=0$

We can re-write as,

$P(k)-3^k=(x-0)(x-1)(x-2)(x-3)(x-4)(x-5)$

$P(k)=3^x+x(x-1)(x-2)(x-3)(x-4)(x-5)$

Put x=6,

$P(6)=3^6+6(6-1)(6-2)(6-3)(6-4)(6-5)$

$P(6)=3^6+6\cdot 5\cdot4\cdot3\cdot2\cdot1$

$P(6)=729+720$

$P(6)=1449$

Sum of digits = 1+4+4+9=18

#Learn more

Polynomial

https://brainly.in/question/3793499, Answered by Lily44.