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2 first: X^2 must be positive for all x=/=0
1 is positive
If A is positive, then good, 2 works
But if A is 0, then we get 1 as answer.
Therefore, 'A' could be 0 or +ve. Out
1 Next: X^2 must be positive for all X=/=0
(-2x will be positive for all negative x)
So, 'A' may be -ve and the value in (1) still remains positive
'A' may also be -ve
Combining, 'A' may be a negative fraction e.g. (-0.0003) and will not work if (x > 2)
1) can be ruled out as x^2 - 2x >0 so A can be + or -ve
2) can be ruled out since if x<1, A can be-ve and statement still satisfied.
Taking both together- A will have to be positive for both statements to hold true. A can only be neagtive in statement 2 if x <1. but if x<1 then x^2 -2x from statement 1 will be < 0 so A willk NEED to be +ve to make this statement true.
remember the 2 statements ALWAYS are to be >0 no matter what value of x. the answer will be E, if for a certain value of x, A can be negative and both statements hold true. i dont think this can happen.