Question

If f(x) is polynomial of degree 4 such that f(1) = 1, f(2) = 2, f(3) = 3. f(4) =4&f(0) = 1
find f(5)​

Answer 1

Answer:

Let us assume,

⇒f(x)=ax

3

+bx

2

+cx+d

Then we get,

⇒f(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 (1) and (2) we get

⇒7a+3b+c=1⟶(5)

solving (1) and (3) we get

⇒2ba+8b+2c=1⟶(6)

solving (1) and (4) we get

⇒63a+15b+3c=15⟶(7)

solving (5) and (7) we get

⇒7a+b=2

This gives a=2,b=−12

And then c=23,d=−12

⇒f(x)=2x

3

−12x

2

+23x−12

⇒f(x)=2×(5)

3

−12×(5)

2

+23(5)−12

=53

Required answer f(5)=53.