106Let f(x) = P(x) - x
This polynomial has 6 roots 1,2,3,4,5,6
So f(x) =k* (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)
= (x-1)(x-2)(x-3)(x-4)(x-5)(x-6) = P(x)-x
(k=1 comparing coeff of x^6)
now putting x=7
6! = p(7) - 7
=> P(7) = 6!+7 = 727
Let P(x)= x6+ ax5+ bx4+ cx3+ dx2+ ex+ f be a polynomial such tht -
P(1)=1, P(2)=2, P(3)=3, P(4)=4, P(5)=5 & P(6)=6.
We need to find the value of P(7).
[A Hint wud do perhaps.] [22]
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3 Answers
106
62this one has been solved sometime back..
f(x)=x
then f(x)-x has 6 roots...
hence f(x)-x = (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)
now solve..
