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let the function p(x) = x6 + ax55 + bx4 +cx3 +dx2 +ex +f be a real polynomial. given leading coefficient is 1 and p(1) = 2,p(2) = 5, p(3) = 10, p(4) = 17, p(5) = 26 and p(6) = 37 then p(10) = ?

HARISH SAHU , 8 Years ago
Grade 12th pass
anser 1 Answers
Nishant Vora

Last Activity: 7 Years ago

Let Q(x) = P(x) – (x^2 + 1)

so clearly x=1,2,3,4,5 and 6 are roots of Q(x)

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

hence P(10) = 9*8*7*6*5*4 + (10^2 + 1) = 60581

Thanks

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