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Let p(x) be a polynomial and p(1)=1 ,p(2)=2 ,p(3)=3,p(4)=5 then find the polynomial and also find p(7).
Asked by renuka.lasya | 24 Feb, 2019, 05:49: PM
Let polynomial p(x) = a x3 + b x2 + c x +d

P(1) = a + b + c+ d = 1  ....................(1)
p(2) = 8a + 4b +2c +d = 2 ..................(2)
p(3) = 27a + 9b + 3c + d = 3 ................(3)
p(4) = 64a +16b +4c + d = 5 ................(4)

Eqn.(4) - eqn(3) : 37a + 7b + c = 2 .......................(5)
Eqn.(3) - eqn(2) : 19a + 5b + c = 1 ......................(6)
Eqn.(2) - eqn(1) : 7a + 3b +c =  1 .......................(7)

Eqn.(6) - Eqn(7) :  12a + 2b = 0  ...........................(8)
Eqn.(5) - Eqn.(6) :  18a +2b =1  ...........................(9)

by solving eqn.(8) and eqn.(9), we get a = 1/6   and b = -1

By substituting values of a and b in eqn.(7), we get c = 17/6

By substituting values of a, b and c in eqn.(1), we get d = -1

hence polynolinal p(x) = (1/6)x3 - x2 +(17/6)x - 1

p(7) = (1/6)73 -72 +(17/6)7 - 1 = 27
Answered by Thiyagarajan K | 24 Feb, 2019, 07:08: PM

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