If the roots of the cubic, `x^3+a x^2+b x+c=0` are three consecutive positive integers, then the value of `a^2/(b+1)` is equal to __________.

Answer

3

Explanation

`n,n+1,n+2`
`Sum=3(n+1)=-a`
`therefore a^(2)=9(n+1)^(2)`
Sum of the roots taken at a time `=pmb`
`therefore n(n+1)+(n+1)(n+2)+(n+2)n+1=b+1`
`n^(2)+n+n^(2)+3n+2+n^(2)+1=b+1`
`thereforeb+1=3n^(2)+6n+3`
`b+1=3(n+1)^(2)=(a^(2))/(3),therefore(a^(2))/(b+1)=3`