Question

# Let f(x) is a cubic polynomial such that f(1)=1,f(2)=2,f(3)=3 and f(4)=16, then f(0) is equal to

A
6
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
6
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
12
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D −12Let us assume:f(x)=ax3+bx2+cx+df(1)=a+b+c+d=1 ………….(1)f(2)=8a+4b+2c+d=2 ………..(2)f(3)=27a+9b+3c+d=3 …………(3)f(4)=64a+16b+4c+d=16 ……….(4)Solving equation (1) & (2), we get7a+3b+c=1 ………..(5)Solving equation (1) & (3), we get26a+8b+2c=2 …….(6)Solving equation (1) & (4), we get63a+15b+3c=15 ……..(7)Solving (5) and (6),6a+b=0Solving (5) and (7)7a+b=2This gives a=2,b=−12,c=23,d=12f(x)=2x3−12x2+23x−12f(0)=2(0)3−12(0)3+23(0)−12f(0)=−12The option [D] is right.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Algebra of Derivatives
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program