Is A positive?
(1) x^2 - 2x + A is positive for all x
(2) Ax^2 + 1 is positive for all x
Would someone please show me how to solve this? Also, what do they mean when they say "for all x"?
Should be 'D'
x^2 - 2x + A > 0
(x-1)^2 + (A -1) > 0
minimum value of (x-1)^2 is 0
in this case A > 1
Keep in mind that we have to find A so that eqn is valid for all x.
for (x-1)^2 >0, positive A very well satisfy the eqn. (x-1)^2 + (A -1) > 0
Hence for x^2 - 2x + A > 0, A will always be > 0
Stmt2:Ax^2 + 1 > 0
for all x, A should be +ve because for negative A, the equation may not hold good.