Question

If y=f(x) is a polynomial function of least degree satisfying simultaneously f(1)=9 f(2)=8 f(3)=7 f(4)=6 f(5)=5 and if f(0) =0 then the value of f(6) equals​

Answer 1

Answer:

Let f(x)=g(x)−x+6

f(1)=5⇒g(1)=0

f(2)=4⇒g(2)=0

f(3)=3⇒g(3)=0

f(4)=2⇒g(4)=0

f(5)=1⇒g(5)=0

therefore g(x) is a function such that g(x)=(x−1)(x−2)(x−3)(x−4)(x−5)

therefore f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)−x+6

f(6)=120