The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
$2$
$3$
$4$
$5$
If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is
Let $x$ and $y$ be two $2-$digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is
Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .$ Then $\mathrm{S}$
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$
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