f-x-ax-4-bx-3-cx-2-dx-e-f-1-2-f-2-3-f-3-4-f-4-5-f-0-25-Then-f-5-Help-me-please-

Question Number 216820 by Ismoiljon_008 last updated on 22/Feb/25

f (x) = {a x}^{4} + {b x}^{3} + {c x}^{2} + d x + e

f (1) = 2

f (2) = 3

f (3) = 4

f (4) = 5

f (0) = 25

T h e n f (5) = ?

H e l p m e, p l e a s e

Answered by BaliramKumar last updated on 22/Feb/25

Commented by Ismoiljon_008 last updated on 22/Feb/25

t h a n k y o u v e r y m u c h

Commented by ArshadS last updated on 22/Feb/25

Some explanation please!

Answered by mr W last updated on 22/Feb/25

f (1) = 2 = 1 + 1

f (2) = 3 = 2 + 1

f (3) = 4 = 3 + 1

f (4) = 5 = 4 + 1

w e c a n s e e

f (x) = x + 1 + g (x) w i t h

g (x) = p o l y n o m i a l o f 4^{t h} d e g r e e a n d

g (1) = g (2) = g (3) = g (4) = 0

\Rightarrow g (x) = A (x - 1) (x - 2) (x - 3) (x - 4)

f (x) = x + 1 + A (x - 1) (x - 2) (x - 3) (x - 4)

f (0) = 1 + A (- 1) (- 2) (- 3) (- 3) = 1 + 24 A = 25

\Rightarrow A = 1

\Rightarrow f (x) = x + 1 + (x - 1) (x - 2) (x - 3) (x - 4)

f (5) = 5 + 1 + 4 \times 3 \times 2 \times 1 = 30 ✓

Commented by ArshadS last updated on 23/Feb/25

t h a n k s s i r!

f (1), f (2), f (3), f (4) a l l a g r e e t h e p a t t e r n : f (x) = x + 1

b u t f (0) = 24 d i s a g r e e s . T h e n w h y i n g e n e r a l t h e

p a t t e r n f (x) = x + 1 i s m a d e ?

Commented by mr W last updated on 23/Feb/25

w e c a n n o t s a y f (x) = x + 1 . b u t w e

c a n s a y

f (x) = x + 1 + A (x - 1) (x - 2) (x - 3) (x - 4)

Commented by ArshadS last updated on 23/Feb/25

T h a n k s t o t e a c h m e s i r!

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