Question

f   3 P x x   3 find the value of P(1), P(2), P(-1), P(-2).

Answer 1

Answer:

Step-by-step explanation:

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=  

6

1

​  

 

∴P(x)=  

6

1

​  

(x−1)(x−2)(x−3)+x

∴P(6)=  

6

1

​  

(5)(4)(3)+6=16

Answer 2

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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