If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be
$2, 2, 3$
$1, 1, -2$
$-2, 3, 3$
$-2, -2, 1$
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 solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are
If $a, b, c$ are real numbers such that $a+b+c=0$ and $a^2+b^2+c^2=1$, then $(3 a+5 b-8 c)^2+(-8 a+3 b+5 c)^2$ $+(5 a-8 b+3 c)^2$ is equal to
If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is