The function k`f(x)=a x^2+b x^2+c x+d` has three positive roots. If the sum of the roots of `f(x)` is 4, the larget possible inegal values of `c//a` is ____________.

Answer

5

Explanation

Let `ax^(2)+bx^(2)+cx+d=0` has roots p,q,r
`pq+qr+rp=(c)/(a)" "(1)`
but `pq+qr+rplep^(2)+q^(2)+r^(2)`
`=(p+q+r)^(2)-2sumpq`
`therefore3(pq+qr+rp)le(p+q+r)^(2)=16`
`therefore3(c)/(a)le16`
`rArr(c)/(a)le(16)/(3)`
`rArr` largest integral value of `(c)/(a)` is 5