Is A Positive ?
1. x^2-2x+A is positive for all x
2. Ax^2 + 1 is positive for all x
Official Explanation -
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. A has to be more than 1.
Statement (2) by itself is insufficient. Ax^2+1 is positive for all even if A is 0.
The correct answer is A
Now how about this -
x^2 -2x + A > 0 for all x
=> (x-1)^2 + (A-1) > 0 for all x
now, lets say if x-1=root5, (x-1)^2 = 5,
A can be 3, hence, the expression becomes 5 + 2 = 7 > 0 ,
Is A positive, answer to question is YES
A can be -3, hence, the expression becomes 5 - 4 = 1 > 0 ,
Is A positive, answer to question is NO
Not sure if I miss something.
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