Tip:A–D to answerE for explanationV for videoS to reveal answer
If f(x) is a polynomial of degree 4, f(n)=n+1 and f(0)=25, then find f(5)=?
- A.
30
(Correct Answer) - B.
20
- C.
25
- D.
None
Explanation
f(x) → 4 degree polynomial
Let
f(x) = λ(x - 1)(x - 2)(x - 3)(x - 4) + (x + 1)
f(0) = λ(-1)(-2)(-3)(-4) + 1 = 25
⇒ λ = 1
f(5) = 6 + 24λ
Put λ = 1
f(5) = 30.
Explanation
f(x) → 4 degree polynomial
Let
f(x) = λ(x - 1)(x - 2)(x - 3)(x - 4) + (x + 1)
f(0) = λ(-1)(-2)(-3)(-4) + 1 = 25
⇒ λ = 1
f(5) = 6 + 24λ
Put λ = 1
f(5) = 30.
