Tricky Problem!
Algebra
Level
4
Find The Interval Of a for which ax^2 + 2ax+1/2 is always positive for every real x .
give your answer as the number of integral values of a which satisfy the constraint.
0
infinitely many
2
many values of a are possible (but not infinite which are not given in the options)
3
1
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1 solution
The Problem Is Quite Simple But Is Tricky .
We Know That The Given Function Will Always Be Positive If Its Discriminant Is Less Than Zero and
coefficient of x^2 is greater than . Now Solving The Conditions We Get 0<a<1/2 .
So We Are Bound To Say That No Integral Value Exists .
But Wait ! . I Have No where said that the given function is a quadratic function hence a = 0 also . if a=0 then function for all x will have positive value .
Hence One Integral Value Of a exists .