Is A positive?
i)x^2-2x+A is positive for all x
ii)Ax^2+1 is positive for all x
reason given < Statement (1) by itself is sufficient. x^2-2x+A = (x-1)^2+(A-1) . For this expression to be always positive (A-1) has to be more than 0.so A has to be more than 1>
A can be any -ive int till (x-1)^2 is greater than (A-1)... ex x=3... 4+A-1>0.. or A>-3
ans shud be E...pl confirm
i think where we have gone wrong is taking + in(x-1)^2+(A-1) as *....
Step by step:
Question: is A>0
is positive for all x
is a function of of upward parabola. We are told that it's positive for all x
, which means that this function is "above" X-axis OR in other words parabola has no intersections with X-axis OR equation x^2-2x+A=0
has no real roots.
Quadratic equation to has no real roots discriminant must be negative --> D=2^2-4A=4-4A<0
is positive for all x
--> when A\geq0
this expression is positive for all x
. So A
can be zero too.
So I think the answer (A) is correct.
NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
25 extra-hard Quant Tests