This is a Test of Mathematics Solution Subjective 76 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Find the set of all values of such that can take all real values.

Now takes all real values if discriminant is allways .

So now we have to find the all values of such that for all |R.

…(i)

Now this is a equation of upside open parabola. If the discriminant is of equation (i) then will always positive.

* Conclusion*:

If , then can take all the values as varies over |R.