Question

P(1)=2,p(3)=4 P(5)=6,P(7)=7 is a vubic polynomial find p(6)

Answer 1

answer

131/16

Step-by-step explanation:

let f(x) = (P(x)-x)

f(1)= P(1)-1= 2-1= 1

f(3)= P(3)-3= 4-3= 1

f(5)= P(5)-5= 6-5=1

f(x)= 1, x=1,3,5

=> f(x) =a(x-1)(x-3)(x-5)

P(x) = a(x-1)(x-3)(x-5)+x

putting x=7,

P(7)= a(6)(4)(2)

=> a= 7/48

therefore, P(6)= (7/48)*(5)(3)(1)+6= 131/16