Question

A monic polynomial P(x) of degree 6 leaves the remainder:-

3 when divided by x-1

9 when divided by x-2

19 when divided by x-3

33 when divided by x-4

51 when divided by x-5

73 when divided by x-6

Find out the value of P(0)

Answer 1

2

Answer 2

Umm. Just solved it right now. The answer is 721. Huehue

Answer 3

if it is so, then I am sorry for my wrong answer. However, I would like to know how you get it. :)

Answer 4

Yes, the answer is 721

Answer 5

@loser66 note that a monic polynomial means that the leading coefficient is equal to 1.

Answer 6

I know:)

Answer 7

So we only have 6 parameters to be solved with the 6 given equations.

Answer 8

yes, I see it now. I am sorry.

Answer 9

:)

Answer 10

I just thought here that P(x) = S(x) + G(x) where 1, 2, 3, 4, 5, and 6 are the zeroes of S(x) then G(x) is the remainder of P(x). Then using the given remainders, we get,

\[G(x) = 2x ^{2} + 1\]

Then

\[P(x) = (x-1)(x-2)(x-3)(x-4)(x-5)(x-6) + 2x ^{2} + 1\]

Substituting 0, we get P(0) = 721

Answer 11

I suppose you got the 2x^2+1 by finitie differences?
@killua_vongoladecimo

Answer 12

Yes, that's what I did.

Answer 13

Clever, that saved you from solving a 6 x 6! :)