Show that if p,q,r,sp,q,r,s are real number and pr=2(q+s)pr=2(q+s) then at-least one of the equations x^2+px+q=0x2+px+q=0 and x^2+rx+s=0x2+rx+s=0 has real roots?
1 Answer
Jan 8, 2018
Please see below.
Explanation:
The discriminant of
and that of
and
=
=
=
and if
As sum of the two discriminants is positive,
at least one of them would be positive
and hence atleast one of the equations