Is A positive?
1. x^2 - 2*x + A is positive for all x
2. A*x^2 + 1 is positive for all x
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
a data from gmat club
This topic has expert replies
-
diebeatsthegmat
- Legendary Member
- Posts: 1119
- Joined: Fri May 07, 2010 8:50 am
- Thanked: 29 times
- Followed by:3 members
-
clock60
- Legendary Member
- Posts: 759
- Joined: Mon Apr 26, 2010 10:15 am
- Thanked: 85 times
- Followed by:3 members
here i got A
is a>0
(1)x^2-2x+a>0 for all x. this is quadratic function, with parabola
according to the st any x resulted in +ve value for function, it means that graph lies above x-axis
and the value of 2^2-4a<0-discriminant
(y=ax^2+bx+c D=b^2-4ac)
4-4a<0.1-a<0, a>1 the answer is yes and it is suff
(2)ax^2+1>0
it is easy here to find both +ve and -ve values for a
say a=1
then x^2+1>0 any time yes
a=-0,5, x=1. the -0,5+1=0,5 again yes but a<0
to me insuff
is a>0
(1)x^2-2x+a>0 for all x. this is quadratic function, with parabola
according to the st any x resulted in +ve value for function, it means that graph lies above x-axis
and the value of 2^2-4a<0-discriminant
(y=ax^2+bx+c D=b^2-4ac)
4-4a<0.1-a<0, a>1 the answer is yes and it is suff
(2)ax^2+1>0
it is easy here to find both +ve and -ve values for a
say a=1
then x^2+1>0 any time yes
a=-0,5, x=1. the -0,5+1=0,5 again yes but a<0
to me insuff
