let f(x) be a cubic polynomial such that f(1)=1 f(2)=2 p(3)= 3, p(4)=

1.	let f(x) be a cubic polynomial such that f(1)=1 f(2)=2 p(3)= 3, p(4)= 5. Find p(6)
Answer» Given P(1)=1,P(2)=2,P(3)=3,P(4)=5 Let f(x)=(P(x)−x) f(1)=P(1)−1=1−1=0 f(2)=P(2)−2=2−2=0 f(3)=P(3)−3=3−3=0 ∴f(x)=0,x=1,2,3 ⇒f(x)=a(x−1)(x−2)(x−3) P(x)=a(x−1)(x−2)(x−3)+x Put x=4 5=a(3)(2)(1)+4 ⇒a= 1/6 ∴P(x)= 1/6(x−1)(x−2)(x−3)+x ∴P(6)= 1/6 (5)(4)(3)+6=16

let f(x) be a cubic polynomial such that f(1)=1 f(2)=2 p(3)= 3, p(4)= 5. Find p(6)

Answer»

Given P(1)=1,P(2)=2,P(3)=3,P(4)=5

Let f(x)=(P(x)−x)

f(1)=P(1)−1=1−1=0

f(2)=P(2)−2=2−2=0

f(3)=P(3)−3=3−3=0

∴f(x)=0,x=1,2,3

⇒f(x)=a(x−1)(x−2)(x−3)

P(x)=a(x−1)(x−2)(x−3)+x

Put x=4

5=a(3)(2)(1)+4

⇒a= 1/6

∴P(x)= 1/6(x−1)(x−2)(x−3)+x

∴P(6)= 1/6 (5)(4)(3)+6=16

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let f(x) be a cubic polynomial such that f(1)=1 f(2)=2 p(3)= 3, p(4)= 5. Find p(6)

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