JEE Main 2014 (Offline) | Quadratic Equation and Inequalities Question 138 | Mathematics

If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$$ (where [$$x$$] denotes the greater integer $$ \le x$$) has no integral solution, then all possible values of a lie in the interval :

$$\left( { - 2, - 1} \right)$$

$$\left( { - \infty , - 2} \right) \cup \left( {2,\infty } \right)$$

$$\left( { - 1,0} \right) \cup \left( {0,1} \right)$$

$$\left( {1,2} \right)$$

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

Let $$\alpha $$ and $$\beta $$ be the roots of equation $$p{x^2} + qx + r = 0,$$ $$p \ne 0.$$ If $$p,\,q,\,r$$ in A.P. and $${1 \over \alpha } + {1 \over \beta } = 4,$$ then the value of $$\left| {\alpha - \beta } \right|$$ is :

$${{\sqrt {34} } \over 9}$$

$${{2\sqrt 13 } \over 9}$$

$${{\sqrt {61} } \over 9}$$

$${{2\sqrt 17 } \over 9}$$

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then $$a\,:b\,:c\,$$ is

$$1:2:3$$

$$3:2:1$$

$$1:3:2$$

$$3:1:2$$