Question

Consider x^2+px+q=0, where p and q are positive numbers. If the roots of the equation differ by 1, then p equals

Answer 1

let m and n are root of equation
m+n=-p
mn=q
given m-n=1
square both side
(m-n)^2=1
(m+n)^2-4mn=1
p^2-1=4q
p^2=1+4q
p=+_root (1+4q)
but p and q are positive
so p=root (1+4q)