Question

Find a polynomial f(x) of degree 2 where f(0)=8, f(1)=12, f(2)=18
A. ` x^(2)+3x-8`
B. `x^(2)-3x+8`
C. `2x^(2)-x+3`
D. `x^(2)+3x+8`

Answer 1

Correct Answer - D
Let the polynomial is ` ax^(2) +bx+c `
Now , f(0)=8
implies c=8
`:.` Equation is ` ax^(2)+ bx+8.`
Again .` f(1)=12 implies a+b+18=12 `
`implies` a+b=14 ................ (i)
and f(2)=18
`implies` 4a + 2b+8=18
`implies 2a +b=5` .....(ii)
On solving Eqs. (i) and (ii) , we get a=1,b=3
`:.` Required equation is ` x^(2)+3x+8`