VITEEE 2012 Paper

Let f(x) = -3 + x - x2
Then, f(x) < 0 for all x because coefficient of x2 < 0 and disc < 0. Thus, LHS of the given equation is always positive whereas the RHS is always less than zero.
Hence, the given equation has no solution.
Alternate Solution:
Given, equation is

9

10

= - 3 + x - x2

Let y =

9

10

, therefore
y = - 3 + x - x2
y = [x2−x+

1

4

] - 3 +

1

4

⇒ y =

11

4

= - (x−

1

2

)2
It is clear from the graph that two curves do not intersect. Hence, no solution exists