Question

If f(x) =ax^ + bx+ c,f(1)= 3,f(2)=7,f(3)=13 . Find the values of a,b and f(0)

Answer 1

f(x)=ax^2+bx+c
put x=1 , 2 and 3 we find
f(1)=a+b+c=3--------------(1)

f(2)=4a+2b+c=7------------------(2)

f(3)=9a+3b+c=13-----------------(3)

equation (2)-(1)
3a+b=7-3=4
3a+b=4----------------(4)

equation (3)-(2)

5a+b=6 -----------(5)

now solve equations (4) and (5)
2a=2
a=1. and b=1

put this value in equation (1)
c=1

now
f(x)=x^2+x+1
put x=0
f(0) =0+0+1=1

hence f(0)=1

Answer 2

f(x)=ax^2+bx+c

put x=1 , 2 and 3 we find

f(1)=a+b+c=3--------------(1)

f(2)=4a+2b+c=7------------------(2)

f(3)=9a+3b+c=13-----------------(3)

equation (2)-(1)

3a+b=7-3=4

3a+b=4----------------(4)

equation (3)-(2)

5a+b=6 -----------(5)

now solve equations (4) and (5)

2a=2

a=1. and b=1

put this value in equation (1)

c=1

now

f(x)=x^2+x+1

put x=0

f(0) =0+0+1=1

hence f(0)=1