Question

Let `px^(2)+qx+r=0` be a quadratic equation `(p,q,r in R)` such that its roots are `alpha and beta`. If `p+q+rlt0,p-q+rlt0 and r gt0`, then the value of `[alpha]+[beta]` is (where[x] denotes the greatest integer x)________.

Answer 1

Correct Answer - -1
Given equation is `px^(2)+qx+r=0`
Let `f(x)=px^(2)+qx+r`
`f(0)=rgt0`
`f(1)=p+q+rlt0`
and `f(-1)=p-q+rlt0`
So, one root lies in (-1,0) and the other in (0, 1).
`rArr [alpha]=-1and[beta]=0`
`rArr[alpha]+[beta]=-1`