Let P(x) be a bi-quadratic polynomial such that the coefficient
of xf is 1, P(1) = 2, P(2) = 4, P(3) = 6 and P(4) = 8, then the value
of P(5) is
14
24
34
44
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Explanation:
here p(n)= 2n for n=1,2,3,4
p(n)-2n=0
let this be another biquardratic polynomial f(n)
f(n)=p(n)-2n
when n=x
f(x)=p(x)-2x
f(x)=0 at x=1,2,3,4
so f(x)= k(x-1)(x-2)(x-3)(x-4)
f(x)=(x-1)(x-2)(x-3)(x-4)
(x-1)(x-2)(x-3)(x-4)=p(x)-2x
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