If the equation $\frac{1}{x} + \frac{1}{{x - 1}} + \frac{1}{{x - 2}} = 3{x^3}$ has $k$ real roots, then $k$ is equal to -
$2$
$3$
$4$
$6$
Let $P(x) = x^3 - ax^2 + bx + c$ where $a, b, c \in R$ has integral roots such that $P(6) = 3$, then $' a '$ cannot be equal to
If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$, then
If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to
Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then
The number of real solution of equation $(\frac{3}{2})^x = -x^2 + 5x-10$ :-