If $a, b, c \in R$ and $1$ is a root of equation $ax^2 + bx + c = 0$, then the curve y $= 4ax^2 + 3bx+ 2c, a \ne 0$ intersect $x-$ axis at
two distinct points whose coordinates are always rational numbers
no point
exactly two distinct points
exactly one point
The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in R$, is (where $\{.\}$ denotes fractional part function)
If $\alpha, \beta $ and $\gamma$ are the roots of equation ${x^3} - 3{x^2} + x + 5 = 0$ then $y = \sum {\alpha ^2} + \alpha \beta \gamma $ satisfies the equation
The condition that ${x^3} - 3px + 2q$ may be divisible by a factor of the form ${x^2} + 2ax + {a^2}$ is
Consider the following two statements
$I$. Any pair of consistent liner equations in two variables must have a unique solution.
$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,