Let [t] denote the greatest integer $$ \le $$ t. Then the equation in x,
[x]² + 2[x+2] - 7 = 0 has :

The set of all real values of $$\lambda $$ for which the quadratic equations,
($$\lambda $$² + 1)x² – 4$$\lambda $$x + 2 = 0 always have exactly one root in the interval (0, 1) is :

If $$\alpha $$ and $$\beta $$ are the roots of the equation
x² + px + 2 = 0 and $${1 \over \alpha }$$ and $${1 \over \beta }$$ are the
roots of the equation 2x² + 2qx + 1 = 0, then
$$\left( {\alpha - {1 \over \alpha }} \right)\left( {\beta - {1 \over \beta }} \right)\left( {\alpha + {1 \over \beta }} \right)\left( {\beta + {1 \over \alpha }} \right)$$ is equal to :

Let f(x) be a quadratic polynomial such that
f(–1) + f(2) = 0. If one of the roots of f(x) = 0
is 3, then its other root lies in :