chetan2u wrote:

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?

(1)

x^2-2x+A is positive for all

x:

f(x)=x^2-2x+A is a function of of upward parabola. We are told that it's positive for all

x -->

f(x)=x^2-2x+A>0, 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 -->

1-A<0 -->

A>1.

Sufficient.

(2)

Ax^2+1 is positive for all

x:

Ax^2+1>0 --> when

A\geq0 this expression is positive for all

x. So

A can be zero too.

Not sufficient.

So I think the answer (A) is correct.

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